Monika Piazzesi Ciaran Rogers Martin Schneider Stanford ... · Money and Banking in a New Keynesian...
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Money and Banking in a New Keynesian Model
Monika Piazzesi Ciaran Rogers Martin SchneiderStanford Stanford Stanford
Belgium, December 2019
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Motivation
Standard New Keynesian model
I central bank controls short rate in household stochastic discount factor
I short rate = return on savings & investment
This paper: New Keynesian model with banking sector
I central bank controls interest rate on fed funds or reserves
I households do not hold these assets directly
I banks hold these assets to back inside money
→ disconnect between policy rate & short rate
Central bank operating procedures:
I chooses regime/reserve supply: scarce vs ample
I matters for effectiveness of monetary policy
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Corridor system with scarce reserves
monetary policy targets fedfunds rate, sets reserve rate
trading desk supplies reserves elastically to meet target
banks’ cost of liquidity > 0, rises if central bank tightens
Reserves
Reserve Demand
Reserve Supply
iM
iF
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Floor system with ample reserves
monetary policy sets reserve rate & quantity of reserves
banks’ cost of liquidity zero, remains zero if central bank tightens
Reserves
Reserve Demand
Reserve Supply
iM, iF
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Implications
Standard NK model
I interest rate is all that matters, plumbing & quantities not important
Banking & short rate disconnect: plumbing & quantities matter
I floor system: interest rate policy only affects banks’ cost of safety
- higher reserve rate, cheaper safe collateral to back inside money,lower cost of liquidity for households, not banks, policy weaker
- quantity of reserves is independent policy tool
I corridor system: interest rate policy also affects banks’ cost of liquidity
- higher interbank rate, implemented with lower reserves (not indep.)
- higher cost of liquidity for households & banks, stronger policy
I both systems
- less scope for multiple equilibria with short-rate disconnect(savings rate adjusts to inflation even if e.g. policy rate at peg)
- nominal assets held by banks matter for output & inflation(banks’ cost of safety depends on all collateral, not just reserves)
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Plan for talk
Transmission in minimal model with disconnect
I Households make payments with CBDC (no banks)
Introduce banks that provide inside money for payments
I Government supplies ample reserves (floor system)
I Scarce reserves (corridor system)
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LiteratureNK models with financial frictions & bankingBernanke-Gertler-Gilchrist 99, Curdia-Woodford 10, Gertler-Karadi 11,
Gertler-Kiyotaki-Queralto 11, Christiano-Motto-Rostagno 12,
Del Negro-Eggertson-Ferrero-Kiyotaki 17, Diba-Loisel 17,
Arce-Nuno-Thaler-Thomas 19
Convenience yields on bonds Patinkin 56, Tobin 61, Bansal-Coleman 96,
Krishnamurthy-Vissing-Jorgensen 12, Andolfatto-Williamson 14, Nagel 15,
Hagedorn 18, Michaillat-Saez 19
Convenience yield on assets that back medium of exchangeKiyotaki-Moore 05, Williamson 12, Venkateswaran-Wright 13,Lenel-Piazzesi-Schneider 19
Bank competition Yankov 12, Driscoll-Judson 13, Brunnermeier-Sannikov 14,
Duffie-Krishnamurthy 16, Bianchi-Bigio 17, Egan, Hortacsu-Matvos 17,
Drechsler-Savov-Schnabl 17, DiTella-Kurlat 17
Recent work on dynamics of the New Keynesian model at ZLBinformation frictions, bounded rationality, fiscal theory, incomplete markets
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Minimal model with short rate disconnect (no banks)
Representative householdI utility separable in labor + CES bundle of consumption & money
I σ = IES for bundles, η = interest elasticity of money demand
I for now, separable in consumption & money: η = σ
I later consider complementarity: η < σ
FirmsI consumption goods = CES aggregate of intermediates
I intermediate goods made 1-1 from labor, Calvo price setting
Government: central bank digital currencyI path or feedback rule for money supply Dt
I path or feedback rule for policy rate iDt = interest rate on money
I lump sum taxes adjust to satisfy budget constraint
Market clearing: goods, money, laborI iSt = short rate in household SDF adjusts endogenously
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Linear dynamics
Steady state with zero inflation
Standard NK Phillips curve & Euler equation, κ = λ(
ϕ + 1σ
)∆pt = β∆pt+1 + κyt
yt = yt+1 − σ(iSt − ∆pt+1 − δ
)Households’ money demand
dt − pt = yt −η
δ− rD
(iSt − iDt −
(δ− rD
))
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Why money does not matter in the standard NK model
∆pt = β∆pt+1 + κyt
yt = yt+1 − σ(iSt − ∆pt+1 − δ
)dt − pt = yt −
η
δ− rD
(iSt − iDt −
(δ− rD
))Solve for (pt , yt , iSt , iDt , dt) given initial condition p0
Standard model
I add 2 policy rules: Taylor rule for iSt , peg for iDt = 0
I quantity of money dt endogenous, adjusts to implement policy rule
→ policy rate = short rate
I money does not matter, system is block recursive:
solve for (pt , yt) given iSt , iDt = 0 and initial condition p0
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Why money matters in CBDC model
∆pt = β∆pt+1 + κyt
yt = yt+1 − σ(iSt − ∆pt+1 − δ
)dt − pt = yt −
η
δ− rD
(iSt − iDt −
(δ− rD
))CBDC model
I adds 2 policy rules: interest on money iDt , quantity of money Dt
I short rate iDt endogenous, satisfies Euler equation
→ disconnect: policy rate 6= short rate
I money matters, system no longer block recursive:
solve for (pt , yt , iSt ) given policy rules iDt and Dt
I familiar special case: NK model with money growth rule & peg iDt = 0
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Disconnect and role of money with banks
standard model: policy rate = short rate, money does not matter
CBDC model: policy rate 6= short rate, money matters
banking model with floor system works like CBDC model
I rules for reserve rate iMt , quantity of reserves Mt
I short rate disconnect: households do not hold reserves
banking model with corridor system
I rules for fed funds rate iFt , peg for reserve rate iMt = 0
I reserves endogenously adjust to implement policy rule→ closer to standard model
I but still short rate disconnect: households do not hold fed funds
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Interest rate policy
Standard model: short rate iSt = policy rate
Transmission of interest rate policy
policy rate+−→
real returnon savings
−−→
output,inflation
Money supplied elastically to implement iSt , fix iDt = 0
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Interest rate policyCBDC model: convenience yield is endogenous wedge
iSt − δ = iDt − rD
policy rate
+δ− rD
η
(pt + yt − dt
)convenience yield, increasing in
velocity = spending / money
Transmission of interest rate policy
policy rate+−→
real returnon savings
−−→
output,inflation
+ ↑ + ↓
convenienceyield
+←−
spending,velocity
⇒ convenience yield dampens effect
Money supply = independent policy instrument
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Local determinacy with interest rate peg
Standard model: many bounded solutions to difference equation
When do we get multiple bounded equilibrium paths?
Taylor principle violated low real rate on savings Euler equation
↗ ↘high inflation ←− high output
Phillips curve
Taylor principle: policy reacts aggressively to high inflation→ high real rate on savings
CBDC model: savings rate = policy rate + convenience yield
higher convenience yield → higher real rate on savings
generalized Taylor principle: LR of savings rate to inflation > 1
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When do we get local determinacy with separable utility?
Taylor rule iDt = rD + φπ∆pt + φy yt + υt
Money supply rule Dt = µDt−1 + PtG , µ ≤ 1
I choose µ,G , rD to achieve zero inflation in steady state
I with µ = 1, G = 0 → constant money supply, nominal anchor
I with µ < 1, no nominal anchor: continuum of st.st. price levels
Unique bounded solution iff
LR(iS , ∆p) =δ− rD
η
(µ
1− µ+
1− β
κ
)+ φπ + φy
1− β
κ> 1
Less scope for multiple equilibria if
I lower semielasticity of money demand η/(δ− rD)
I more nominal asset rigidity in balance sheet: higher µ
I prices more sticky: lower λ
I more aggressive inflation response: higher φπ
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Cost channel
Consumption & money complements in utility
I nonseparable utility with η < σ
I higher cost of liquidity iSt − iDt makes shopping less attractive
→ reduce consumption, increase leisure/decrease labor
→ lower output, higher inflation
Effect of higher policy rate on cost of liquidity iSt − iDtI standard model: higher iSt with fixed iDt → higher cost
I CBDC model: higher iDt + imperfect pass-through → lower cost
Numerical example
I δ = 4%, rD = 1.6%, σ = 1, η = .2, standard cost & Calvo pars
I constant money supply
I Taylor rule with coefficient 1.5 on inflation, .5 on past short rate
I compare impulse responses to 25bp monetary policy shock
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IRFs to 25 bp monetary policy shock: standard model
0 4
-0.1
-0.09
-0.08
% d
evia
tions
from
SS
price level
0 4
-0.4
-0.3
-0.2
-0.1
0
% d
evia
tions
from
SS
output
0 4
-4
-2
0
% d
evia
tions
from
SS
money
0 4quarters
-0.3
-0.2
-0.1
0
% p
.a.
inflation
0 4quarters
0
0.2
0.4
% p
.a.
policy rate
0 4quarters
0
0.2
0.4
% p
.a.
conv. yield
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IRFs to 25 bp monetary policy shock: standard vs CBDC
0 4
-0.1
-0.09
-0.08
-0.07
-0.06%
dev
iatio
ns fr
om S
Sprice level
0 4
-0.4
-0.3
-0.2
-0.1
0
% d
evia
tions
from
SS
output
0 4
-4
-2
0
% d
evia
tions
from
SS
money
0 4quarters
-0.3
-0.2
-0.1
0
% p
.a.
inflation
0 4quarters
0
0.2
0.4
0.6
% p
.a.
policy rate
0 4quarters
0
0.2
0.4
0.6
% p
.a.
conv. yield
standardCDBC
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IRFs to 25 bp monetary policy shock: standard vs CBDC
0 4 8 12 16 20
-0.1
-0.09
-0.08
-0.07
-0.06%
dev
iatio
ns fr
om S
Sprice level
0 4 8 12 16 20
-0.4
-0.3
-0.2
-0.1
0
% d
evia
tions
from
SS
output
0 4 8 12 16 20
-4
-2
0
% d
evia
tions
from
SS
money
0 4 8 12 16 20quarters
-0.3
-0.2
-0.1
0
% p
.a.
inflation
0 4 8 12 16 20quarters
0
0.2
0.4
0.6
% p
.a.
policy rate
0 4 8 12 16 20quarters
0
0.2
0.4
0.6
% p
.a.
conv. yield
standardCDBC
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NK Model with Bankscentral bank provides ample reserves (”floor system”)
I reserves are special as collateral, not needed for liquidity
I monetary policy targets reserve rate
Reserves
Reserve Demand
Reserve Supply
iM, iF
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Banking sector
Balance sheetAssets Liabilities
M Reserves Money DA Other assets Equity
Shareholders maximize present value of cash flows
Mt−1(
1 + iMt−1
)−Mt + At−1
(1 + iAt−1
)− At −Dt−1
(1 + iDt−1
)+Dt
Costless adjustment of equity
Leverage constraint: Dt ≤ ` (Mt + ρAt)I ρ < 1 other assets are lower quality collateral to back (inside) money
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Bank optimization: perfect competition
Nominal rate of return on equity = iStI banks equate returns on assets & liabilities to cost of capital iStI γt = multiplier on leverage constraint
Optimal portfolio choice: assets valued as collateral
iSt = iMt + `γt
(1 + iSt
)iSt = iAt + ρ`γt
(1 + iSt
)Optimal money creation: money requires leverage cost
iSt = iDt + γt
(1 + iSt
)⇒ Marginal cost pricing of liquidity
iSt − iDt =1
`
(iSt − iMt
)
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Bank market power
Many monopolistically competitive banks
Households care about CES bundle of deposit varieties
Dt =
(∫ (D it
)1− 1ηb
) 1
1− 1ηb
I ηb = elasticity of substitution between bank accounts
⇒ Constant markup over marginal cost
iSt − iDt =ηb
ηb − 1
1
`
(iSt − iMt
)
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Equilibrium with ample reserves
Government: floor system with ample reservesI path or rule for supply of reserves Mt
I path or rule for interest rate on reserves iMt
Market clearing for reserves & other bank assetsI exogenous path Ar
t of real assets, so At = PtArt
I stands in for borrowing by firms or against housing
Characterizing equilibriumI NK Phillips curve & Euler equation unchanged
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Dynamics with ample reserves
Interest rate pass-through: reserve rate to short rate
iSt − δ = iMt − rM +δ− rM
η
(pt + yt − dt
)I reserves back inside money, inherit convenience yield of deposits
Money supply
dt =M
M + ρAmt +
ρA
M + ρAat
I reserves a separate policy instrument: QE stimulates economy!
I other bank assets also matter: bad loan shocks contractionary
⇒ Works like CBDC model, but coefficients depend on banking system
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Banking with scarce reserves
Banks manage liquidity
I deposit outflow/inflow λDt to/from other banks
I iid liquidity shock λ has mean zero, cdf G with bounded support
I satisfy leverage constraint after deposit inflow/outflow
I borrow/lend in competitive fed funds market at rate iF
Assets valued as collateral, reserves also for liquidity
Government:
I path or rule for fed funds rate iFt , reserve rate iM ; here iM = 0
I reserve supply adjusts to meet interest rate targets
Market clearing for reserves, Fed funds
I reserves scarce: quantity small relative to support of liquidity shocksI otherwise iF = iM & no active Fed funds market, back to floorI government selects type of equilibrium
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Dynamics with scarce reserves
Interest rate pass-through: fed funds rate to short rate
iSt − δ = iFt − rM +δ− rM
η
(pt + yt − dt
)Inside money in reserveless limit: share of reserves in bank assets → 0
dt =η
η + εat +
ε
η + ε
(pt + yt −
η
rF
(iFt − rF
))I ε = function of bank technology parameters
⇒ Works like CBDC model with more elastic money supply
Numerical example to compare floor & corridor system
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25bp increase in policy rate: corridor vs floor systems
0 4
-0.25
-0.2
-0.15
-0.1
-0.05%
dev
iatio
ns fr
om S
Sprice level
0 4
-0.3
-0.2
-0.1
0
% d
evia
tions
from
SS
output
0 4
-1
-0.5
0
% d
evia
tions
from
SS
money
0 4quarters
-0.4
-0.2
0
% p
.a.
inflation
0 4quarters
0
0.2
0.4
0.6
% p
.a.
policy rate
0 4quarters
-0.04
-0.02
0
0.02
0.04
0.06
0.08
% p
.a.
conv. yield
corridorfloor
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Conclusion
Disconnect between policy rate and short rateI convenience yield is endogenous wedge, changes transmission
I less scope for multiple equilibria, even without Taylor principle
I policy weaker if more nominal rigidities in balance sheets
Bank models vs CBDC modelI same basic transmission mechanism
I difference to standard model depends on details of banking system:F nominal rigidities in bank balance sheets, bank market power
F liquidity management & elasticity of deposit supply
Corridor vs floor systemI with cost channel, significant differences in IRFs
I corridor system closer to standard model than floor system