Download The central-bank balance sheet as an instrument of monetary policy

Introduction
The model
Interpretation
The central-bank balance sheet as
an instrument of monetary policy
V. Cúrdia and M. Woodford
Lecture 2
Jonathan Benchimol1
This presentation does not necessarily re‡ect the views of the Bank of Israel
February 2016
1 Bank
of Israel and EABCN
Jonathan Benchimol
Bank of Israel
Introduction
The model
Interpretation
Research questions
Findings
Literature review
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Cúrdia and Woodford (2009). Credit frictions and optimal
monetary policy, BIS Working Papers 278.
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Cúrdia and Woodford (2010c). Credit spreads and monetary
policy. Journal of Money, Credit and Banking 42(s1), 3–35.
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Eggertsson and Woodford (2003). The zero bound on interest
rates and optimal monetary policy. Brookings Papers on
Economic Activity 2003(1), 139–211.
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Woodford (2003). Interest and prices: foundations of a theory
of monetary policy. Princeton University Press, Princeton.
2 / 31
Introduction
The model
Interpretation
Research questions
Findings
Some questions
I
Monetary policy is ordinarily considered solely in terms of the
choice of an operating target for a short-term nominal interest
rate.
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During the crisis, the appropriate size of the central bank’s
balance sheet was part of the debate (Fig. 1 and Fig. 2).
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Does it make sense to regard the supply of bank reserves (or
perhaps the monetary base) as an alternative or superior
operating target for monetary policy ?
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Does this (as some would argue) become the only important
monetary policy decision once the overnight rate (the federal
funds rate) has reached the zero lower bound ?
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How should this additional potential dimension of policy be
used ?
3 / 31
Introduction
The model
Interpretation
Research questions
Findings
Cúrdia and Woodford: what do they do ?
I
They analyze additional dimensions of central bank policy
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size and composition of the central-bank balance sheet
interest rate paid on reserves
operating target for the federal funds rate
4 / 31
Introduction
The model
Interpretation
Research questions
Findings
Cúrdia and Woodford: what do they …nd ?
I
no role for quantitative easing as an additional tool of
stabilization policy, even at ZLB.
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there may be a role for central-bank credit policy, or for
targeted asset purchases, when private …nancial markets are
su¢ ciently deteriorated.
I
when they are, as indicated by signi…cant increases in
interest-rate spreads, one must be cautious in drawing
conclusions about the welfare consequences of credit policy.
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ZLB is neither necessary nor su¢ cient for active credit policy
to be welfare-improving.
5 / 31
Introduction
The model
Interpretation
Sectors and types
Central bank policy
Welfare
Assumptions
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No endogenous variations in the capital stock.
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No distinction between the household and …rm sectors of the
economy
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Instead they treat all private expenditure as the expenditure of
in…nite-lived household-…rms
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No consequences of investment spending for the evolution of
the economy’s productive capacity
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Instead they treat all private expenditure as if it were
non-durable consumer expenditure
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Monopolistic competition in goods markets.
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Sticky prices à la Calvo (1983)
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Two household types: savers (s) and borrowers (b).
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Introduction
The model
Interpretation
Sectors and types
Central bank policy
Welfare
Representative household
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Households seek to maximize:
+∞
E0
8
<
∑ β t : u τ ( i ) ( ct ( i ) ; ξ t )
t =0
t
Z1
υτt (i ) (ht (i, j ) ; ξ t ) dj
0
where τ t (i ) indicates household’s type in period t and
u
τ t (i )
( ct ( i ) ; ξ t ) =
c1
στ 1
(C̄tτ )
1 στ 1
9
=
;
(1)
στ 1
(2)
where C̄tτ is an exogenous type-speci…c disturbance indicating
variation in aggregate spending opportunities.
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The index ct (i ) is a Dixit–Stiglitz aggregator of the
household’s purchases of di¤erentiated goods, with elasticity
of substitution θ between any two goods.
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Introduction
The model
Interpretation
Sectors and types
Central bank policy
Welfare
Household’s types
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Each agent’s type τ t (i ) evolves as an independent two-state
Markov chain.
Each period, an event occurs with probability 1 δ (for
0 δ < 1) which results in a new type for the household
being drawn; otherwise it remains the same as in the previous
period.
When a new type is drawn, it is b with probability π b > 0 and
s with probability π s < 1, where π b + π s = 1.
ucb (c; ξ ) > ucs (c; ξ ) for all levels of expenditure c in the range
that occur in equilibrium.
A change in a household’s type changes its relative impatience
to consume.
Current impatience of households to consume is changed by
the exogenous disturbances C̄tτ .
8 / 31
Introduction
The model
Interpretation
Sectors and types
Central bank policy
Welfare
Representative …rm
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Continuum of di¤erentiated goods, each produced by a
monopolistically competitive supplier, with a production
technology for each good j of the form
yt (i ) = At ht (j )1/φ
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(3)
where φ indicates the degree of diminishing returns, and At is
an exogenous productivity shock, common to all goods.
The household similarly supplies a continuum of di¤erent
types of specialized labor, indexed by j, that are hired by …rms
in di¤erent sectors of the economy
ψ τ 1 +v
υτt (i ) (ht (i, j ) ; ξ t ) =
h H̄t v
(4)
1+v
where v is the inverse of the Frisch elasticity of labor supply
for both types, and H̄t is an exogenous disturbance, also
common to both types.
9 / 31
Introduction
The model
Interpretation
Sectors and types
Central bank policy
Welfare
Summarizing the economy (1)
λbt
= 1 + itd (1 + ω t ) βEt
"
( δ + (1
+ (1
λb
δ) π b ) Πtt++11
δ ) (1
λs
π b ) Πtt++11
#
(5)
where λbt is the marginal utility of expenditure of borrowers, itb is
b
d
the deposit/policy rate, ω t = i1t +iidt is the spread between
t
borrowing and deposit rates, Πt is the gross in‡ation rate, and λst
is marginal utility of expenditure of savers de…ned as
"
#
λbt+1
1
δ
π
(
)
b Π t +1
λst = 1 + itd βEt
(6)
λs
+ (δ + (1 δ) (1 π b )) Πtt++11
10 / 31
Introduction
The model
Interpretation
Sectors and types
Central bank policy
Welfare
Summarizing the economy (2)
Kt
=
Λ λbt , λst
p
(1 + ω y ) ψµwt H̄t v
µ
λ̃ λbt , λst
h
i
θ (1 + ω )
+αβEt Πt +1 y Kt +1
Yt
At
1 +ω y
where Kt is an arti…cial variable used in recursive version of
in‡ation dynamics, Λ and λ̃ are di¤erent weighted average
functions, and µwt is the wage markup.
h
i
Ft = Λ λbt , λst (1 τ t ) Yt + αβEt Πtθ+11 Ft +1
(7)
(8)
where Ft is an arti…cial variable used in recursive version of
in‡ation dynamics, and τ t is the marginal tax rate.
11 / 31
Introduction
The model
Interpretation
Sectors and types
Central bank policy
Welfare
Summarizing the economy (3)
Real per capita private debt evolves according to
(1 + π b ω t ) bt = π b π s B λbt , λst , Yt , ∆t ; ξ t
+ δ bt
Yt = π b C̄tb λbt
σb
1
(1 + ω t
π b btg
g
1 ) + π b bt 1
+ π s C̄ts (λst )
σs
1 + itd
Πt
+ Gt + Ξ t
(9)
1
(10)
where btg is the total outstanding real public debt, Gt represents
government consumption, and Ξt is the total intermediation
resource costs, including both private and central bank.
∆t = α∆t
θ (1 + ω y )
1 Πt
+ (1
α)
1
αΠtθ
1 α
1
! θ (1θ+ω1 y )
(11)
where ∆t measures price dispersion.
12 / 31
Introduction
The model
Interpretation
Sectors and types
Central bank policy
Welfare
Summarizing the economy (4)
1
1
αΠtθ
1 α
=
{
Ft
Kt
θ 1
1 +θω y
(12)
η 1
+ Ξ̃t+
(13)
where Lcb
is
the
real
quantity
of
lending
by
the
central
bank
to
the
t
private sector, χ̃t (χ̃t+ ) is a multiplicative (additive) shock to
default rate, Ξ̃t (Ξ̃t+ ) is a multiplicative (additive) private
intermediation resource cost shock.
ω t = (1 + {) χ̃t bt
Ξt = Ξ̃t bt
Lcb
t
Lcb
t
η
+ χ̃t+ + η Ξ̃t bt
+ Ξ̃t+ bt
Lcb
t
cb
Lcb
+ Ξ̃cb
t
t Lt
(14)
where Ξ̃cb
t is a resource cost function.
13 / 31
Introduction
The model
Interpretation
Sectors and types
Central bank policy
Welfare
Financial intermediaries (1)
The private intermediaries resource cost, given the satiation of
reserves, is given by:
Ξpt (L; ξ t ) = Ξ̃t Lt + Ξ̃t+ L
η
where L is the amount of privately intermediated credit, and η
Fraudulent credit loss is
χ (L; ξ t ) = χ̃t L1t +{ + χ̃t+ L
(15)
1.
(16)
where { 0.
Central bank lending resource cost
Ξcb
Lcb
t
where η cb
η cb
= Ξ̃cb
t L
(17)
1.
14 / 31
Introduction
The model
Interpretation
Sectors and types
Central bank policy
Welfare
Financial intermediaries (2)
Intermediary chooses dt such that
1 + itd dt = 1 + itb Lt + (1 + itm ) mt
(18)
where mt is the quality of real reserves held at the central bank
paying a nominal interest yield itm .
Deposits not used to …nance either loans or the acquisition of
reserve balances are distributed as earnings to its shareholders
dt
mt
Lt
χt (Lt )
Ξpt (Lt ; mt )
(19)
Market-clearing in the credit market requires that
bt = Lcb
t + Lt
(20)
15 / 31
Introduction
The model
Interpretation
Sectors and types
Central bank policy
Welfare
Financial intermediaries (3)
F.O.C. /Lt
∂Ξpt (Lt ; mt ) ∂χt (Lt )
i b itd
+
= ωt = t
∂Lt
∂Lt
1 + itd
F.O.C. /mt
∂Ξpt (Lt ; mt )
itb itm
= δm
t =
∂mt
1 + itd
(21)
(22)
Eq. 22 determines the equilibrium di¤erential between the interest
paid on deposits and that paid on reserves at the central bank.
16 / 31
Introduction
The model
Interpretation
Sectors and types
Central bank policy
Welfare
Dimensions of central-bank policy
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In the model, central bank’s liabilities consist of the reserves
Mt (which is also the monetary base in the simple model).
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Central bank’s holdings of government debt is mt Lcb
t (two
variables chosen by the central bank) where 0 Lcb
mt
t
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Positive quantity of public debt remains in the portfolios of
g
households2 : mt
Lcb
t + bt
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Strong assumption: itm is assumed to be equal to the one
private sector request reserves (i.e. the central bank receives
the market-determined yield). Then, at equilibrium, itm = itb .
In other words, the central bank cannot use this instrument in
the model.
2 This
constraint is never binding.
17 / 31
Introduction
The model
Interpretation
Sectors and types
Central bank policy
Welfare
Instruments of central-bank policy
I itd
is determined at each period by the system
mt
δm
t
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mtd (Lt ; δm
t )
0
(23)
where mtd (L; δm
t ) represents the demand for reserves which
equals the satiation level (m̄t (L)) when δm
t = 0.
For institutional reasons, it is not possible for the central bank
to pay a negative interest rate on reserves, thus implying that
0 itm itd .
To summarize, the central bank can play with the quantity of
reserves Mt that are supplied, with the interest rate paid
on those reserves itm (disabled here), and with the
breakdown of central-bank assets between government
debt and lending Lcb
t to the private sector.
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Introduction
The model
Interpretation
Sectors and types
Central bank policy
Welfare
Welfare objective
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Optimal policy is considered: the objective of policy is the
maximization of average expected utility such as
+∞
Et 0
∑
βt
t0
Ut
(24)
t =t 0
where Ut refers to the household’s utility function used in Eq.
1.
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See the paper for the demonstration why arguments
Ut = U (Yt , Ωt , Ξt , ∆t ; ξ t ) , where Ωt = λbt /λst , su¢ ce to
determine welfare, and the way each of them a¤ects welfare.
19 / 31
Introduction
The model
Interpretation
Reserve-supply policy
Optimal credit policy
Conclusion
Summary
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Optimal policy with regard to the supply of reserves: taking as
given (for now) the way in which the central bank chooses its
operating target for the policy rate itd , and the
state-contingent level of central-bank lending to the private
sector (Lcb
t ).
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Simple result: optimal policy requires that intermediaries be
satiated in reserves, i.e., that 8t Mt /Pt
m̄t (Lt ).
20 / 31
Introduction
The model
Interpretation
Reserve-supply policy
Optimal credit policy
Conclusion
Is a reserve supply target needed?
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E¢ cient condition: itm = itd i.e. δm
t =0
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When the central bank acts to implement its target for the
policy rate through open-market operations, it will
automatically have to adjust the supply of reserves so as to
satisfy δm
t = 0.
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No need of FOMC decision, bank’s sta¤ in charge of carrying
out the necessary interventions is su¢ cient.
21 / 31
Introduction
The model
Interpretation
Reserve-supply policy
Optimal credit policy
Conclusion
Is there a role for quantitative easing?
I
By construction, the model implies that it is desirable to
ensure that the supply of reserves never falls below a certain
satiation level: m̄t (Lt ).
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It then implies that there is no bene…t from supplying reserves
beyond that level.
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However, it can be desirable to supply reserves beyond
m̄t (Lt ) if this is necessary in order to make the optimal
quantity of central bank lending to the private sector
consistent with 0 Lcb
mt .
t
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See Fig. 3.
22 / 31
Introduction
The model
Interpretation
Reserve-supply policy
Optimal credit policy
Conclusion
An other dimension of central-bank policy
Adjustment of the composition of the asset side of the central
bank’s balance sheet (taking as given the overall size of the
balance sheet)
Ξ̄pt (Lt ) = Ξpt (Lt ; m̄t (Lt ))
(25)
ω̄ t (Lt ) = ω t (Lt ; m̄t (Lt ))
(26)
Specifying the evolution of Ξpt and ω t as functions of the evolution
of aggregate private credit, the equilibrium conditions of the model
do not refer to the quantity of reserves or to the interest rate paid
on reserves.
23 / 31
Introduction
The model
Interpretation
Reserve-supply policy
Optimal credit policy
Conclusion
"Treasuries only"
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According to the traditional doctrine of “Treasuries only”, the
central bank should not vary the composition of its balance
sheet as a policy tool;
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Instead, it should avoid both balance-sheet risk and the
danger of politicization by only holding (essentially riskless)
Treasury securities at all times, while varying the size of its
balance sheet to achieve its stabilization goals for the
aggregate economy.
24 / 31
Introduction
The model
Interpretation
Reserve-supply policy
Optimal credit policy
Conclusion
Eggertsson and Woodford (2003)
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Eggertsson and Woodford (2003) show that assets purchased
by the central bank have no consequences for the equilibrium
evolution of output, in‡ation or asset prices.
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This irrelevance result does not hold, however, in the presence
of credit frictions of the kind assumed here.
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Proof: the di¤erence between the economy’s evolution under
an optimal credit policy and under the constraint of
“Treasuries only” (Fig. 6 to Fig. 12).
25 / 31
Introduction
The model
Interpretation
Reserve-supply policy
Optimal credit policy
Conclusion
Relaxing the “Treasuries only” restriction (1)
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What is the marginal increase in the value of the welfare
objective (Eq. 24) that is achieved by a marginal increase in
Lcb
t above zero in some period.
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The marginal cost of central-bank lending required for
) is reported in …gures
“Treasuries only” to be optimal (Ξcb,crit
t
such as
i
ϕω,t h p 00
00
p0
Ξcb,crit
=
Ξ̄
L
+
Ξ̄
L
+
χ
L
(27)
(
)
(
)
(
)
t
t
t
t
t
t
t
ϕΞ,t
0
where Ξ̄pt is the marginal resource cost of lending by private
intermediaries.
26 / 31
Introduction
The model
Interpretation
Reserve-supply policy
Optimal credit policy
Conclusion
Relaxing the “Treasuries only” restriction (2)
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Four di¤erent possible purely …nancial disturbances, each of
which will be assumed to increase the value of ω̄ t (L̄) by the
same number of percentage points:
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Additive shock: translates the schedule ω̄ t (Lt ) vertically by a
constant amount;
Multiplicative shock: multiply the entire schedule ω̄ t (Lt ) by
some constant factor greater than 1.
Ξ shock: disturbances that change the function Ξ̄t (Lt );
χ shock: disturbances that change the function χt (Lt ).
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Fig. 4 shows that the degree to which a …nancial disturbance
provides a justi…cation for active central-bank credit policy
depends very much on the reason for the increase in spreads.
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Fig. 5 shows how optimal vs. Taylor rules react, with or
without ZLB.
27 / 31
Introduction
The model
Interpretation
Reserve-supply policy
Optimal credit policy
Conclusion
Optimal credit policy under alternative …nancial
disturbances
I
Optimal state-contingent evolution of central-bank lending
Lcb
t , only the constraint that it be non-negative is imposed,
and resource costs of loan origination and central-bank
monitoring are taken into account.
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Existence of a competitive loan market is still assumed :
central-bank lends at the same (market-clearing) interest rate
itb as the private intermediaries, who continue to lend even
when the central-bank lends as well.
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As previous results suggest, the degree to which active credit
policy is optimal varies with the nature of the …nancial
disturbance.
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See Fig. 6 to Fig. 12.
28 / 31
Introduction
The model
Interpretation
Reserve-supply policy
Optimal credit policy
Conclusion
Segmented credit markets
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In reality, there are many distinct credit markets, and many
di¤erent parties to which the central-bank might consider
lending.
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For each of the segmented credit markets, we have Eq. 25
and Eq. 26.
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Lending might be justi…ed in one or two speci…c markets while
the corner solution remained optimal in the other markets.
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Aggregate conditions will be one factor that a¤ects the
shadow value of marginal reductions in the size of credit
spreads : market-speci…c multiplier ϕω,t .
29 / 31
Introduction
The model
Interpretation
Reserve-supply policy
Optimal credit policy
Conclusion
Conclusion (1)
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Analysis of additional dimensions of central-bank policy.
Explicitly modeling the role of the central-bank balance sheet
don’t imply any role for quantitative easing as an additional
tool of stabilization policy, even when ZLB is reached.
Maybe a role for central-bank credit policy (or for targeted
asset purchases) when private …nancial markets are
su¢ ciently impaired.
It is only at times of unusual …nancial distress (i.e. when
…nancial markets fail to ful…ll that function) that active credit
policy will have substantial bene…ts.
Even when …nancial markets are seriously disrupted, as
indicated by signi…cant increases in interest-rate spreads, one
must be cautious in drawing conclusions about the welfare
consequences of credit policy.
30 / 31
Introduction
The model
Interpretation
Reserve-supply policy
Optimal credit policy
Conclusion
Conclusion (2)
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ZLB does not necessarily involve welfare-improving active
credit policy.
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Interest-rate policy decisions are not constrained in any direct
way by decisions about either the size or composition of the
central bank’s balance sheet, as long as the central bank is
willing to adjust the interest rate paid on reserves
appropriately.
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Fed "exit" strategy and nominal interest rate increase are not
necessarily linked.
31 / 31