Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Some Unpleasant

Central Bank Balance Sheet Arithmetic

Saroj Bhattarai

University of Texas at Austin

Keio UniversityOct 31, 2017

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Motivation

I Central bank balance sheet size and composition have changedI Result of unconventional monetary policy by major central banks

I Composition change has generated mismatchesI Interest-bearing short-term liabilities (reserves)I Long-term (or foreign currency) assets

I Such maturity (or currency) mismatches can generate non-trivial�uctuations in central bank income and remittances to the Treasury

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Research questions

I Do these mismatches a�ect conventional monetary policy?I What monetary and �scal policy regime can make it matter?

I If so, how exactly does it constrain conventional monetary policy?I How is the path of interest rate (or exchange rate) a�ected?

I What are the implications for monetary policy transmission?I Use an otherwise standard dynamic GE modelI Transmission of a current monetary policy shock (surprise shock)I Transmission of a monetary policy news shock (forward guidance shock)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Related literature

I Monetary and �scal policy interactionsI Unpleasant monetarist arithmetic and �scal theory of the price level(Sargent and Wallace (1981), Sims (1994), Woodford (1995), ... )

I Central bank balance sheet and monetary policyI Pre-crisis (Sims (2004), Sims (2005), Jeanne and Svensson (2007),Berriel and Bhattarai (2009))

I QE, interest on reserves, and implications (Hall and Reis (2013), DelNegro and Sims (2015), Bhattarai, Eggertsson, and Gafarov (2016))

I Forward guidance puzzle and resolutionsI Del Negro, Giannoni, and Patterson (2015), Mckay, Nakamura, andSteinsson (2016), ...

I Correlation between nominal rate and in�ation/real rateI Neo-Fisherism (Williamson (2015))

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

US Federal Reserve

2002 2004 2006 2008 2010 2012 2014 2016Years

-30

-20

-10

0

10

20

30

40

Perc

ent o

f N

omin

al G

DP(

%)

(a) Assets and Liabilities

Total AssetsTreasury Security(<1 year)Treasury Security(<5 year)Treasury Security(>5 year)

Total LiabilitiesCurrencyReserves

2002 2004 2006 2008 2010 2012 2014 2016Years

-40

-20

0

20

40

60

80

100

120

140

USD

bill

ions

(b) Income and

Transfers to Government

Income from Treasury SecuritiesIncome from MBSsTotal Net IncomeTransfers to Treasury

Interest on ReservesInterest on Repurchase Agreement

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Bank of Japan

2002 2004 2006 2008 2010 2012 2014 2016Years

-100

-80

-60

-40

-20

0

20

40

60

80

100

Perc

ent o

f N

omin

al G

DP(

%)

(a) Assets and Liabilities

Total AssetsJapanese Government BondsForeign Currency Assets

Total LiabilitiesCurrencyReserves

2002 2004 2006 2008 2010 2012 2014 2016Years

-1

-0.5

0

0.5

1

1.5

2

JPY

trill

ions

(b) Income and

Transfers to Government

Interest on Government SecuritiesNet Gains on Foreign Currency AssetsNet Gains on Sale of JGSTotal Net IncomeTransfers to Government

Interest on Repurchase AgreementsProvisions for Possible Losses

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Swiss National Bank

2002 2004 2006 2008 2010 2012 2014 2016Years

-150

-100

-50

0

50

100

150

Perc

ent o

f N

omin

al G

DP(

%)

(a) Assets and Liabilities

Total AssetsGold HoldingsForeign Currency Investments

2002 2004 2006 2008 2010 2012 2014 2016Years

-30

-20

-10

0

10

20

30

40

CH

F bi

llion

s

(b) Income and

Transfers to Government

Net Income fromGold HoldingsNet Income fromForeign Currency Positions

Total LiabilitiesCurrencyReserves

Total Net IncomeTransfers to GovernmentDistributionReserves

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Closed economy model

I Nominal central bank �ow budget constraint

Q1tBt−1−Lt−1−Mt−1−PtTt = Q2tBt −Q1tLt −Mt

where Pt is the price level

I Balance sheet variables (model of maturity mismatch)I Mt : non-interest bearing liabilitiesI Lt : one-period liabilities with Q1t its priceI Bt : two-period assets with Q2t its price

I Monetary/�scal policy interaction variableI Tt : central bank transfer to the Treasury

I Conventional monetary policy instrumentI Q1t : one-period bond price

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Closed economy model

I Real �ow budget constraint

Q1tbt−1Π−1t − lt−1Π−1t −mt−1Π−1t −Tt = Q2tbt −Q1t lt −mt

where Πt is gross in�ation

I Complete market asset-pricing

Q1t = Et

[ζt,t+1Π−1t+1

], Q2t = Et

[ζt,t+1Q1t+1Π−1t+1

]where ζt,t+1 is the stochastic discount factor

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Closed economy model

I Approximate the budget constraint and asset pricing conditions andabstract from cash/seigniorage

I Expectations hypothesis: Q2t = Q1t +EtQ1t+1

I Budget constraint

bN,t =1

βbN,t−1−

1

βTt +bRN,t

where net interest income

RN,t ≡ Q1t −βEtQ1t+1

I Note some featuresI Su�cient state variable: bN,t ≡ β bt − ltI In�ation does not appear (both assets and liabilities nominal)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Closed economy model

I PV form

bN,t−1 =∞

∑t=0

βtTt −βb

∞

∑t=0

βtRN,t

where net interest income

RN,t ≡ Q1t −βEtQ1t+1

I Consider a �xed PV of Tt (As in Sargent and Wallace (1981))I This is a balance sheet constrained central bank

I When a closed economy central bank is balance sheet constrained

I Increase in RN,t today leads to a decrease in future (similar to higherseigniorage today leading to lower seigniorage in future)

I Interest rate path in future gets constrained (similar to in�ation)I This is unpleasant central bank balance sheet arithmetic

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

GE modelClosed economy model

I Standard GE model to assess policy and macro implicationsI Endogenous determination of in�ation and output

I Monetary policy rulesI Standard interest rate policy ruleI Central bank transfer rule

I Policy experimentsI Monetary policy surprise shockI Monetary policy news shock (forward guidance)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Households

I Representative household maximizes

E0

∞

∑t=0

βtU (ct ,ht)

where ct is a CES aggregate of di�erentiated varieties ct(i)

I Household �ow budget constraint

lHt−1Π−1t −Q1tbHt−1Π−1t = Q1t l

Ht −Q2tb

Ht + ct −wtht −ϕt + τt

where wt is real wages, ϕt is pro�ts from �rms, and τt is netlump-sum taxes from the Treasury

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Firms

I Continuum of monopolistically competitive �rms

I Firm i ∈ [0,1] produces output yt(i) using labor

I Firm i sets prices Pt (i) for its good facing demand

yt(i)

yt=

(Pt(i)

Pt

)−ν

and subject to cost of adjusting prices

d

(Pt (i)

Pt−1 (i)

)I Firm i maximizes expected discounted pro�ts

E0

∞

∑t=0

ζ0,tϕt (i)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Monetary policy

I Central bank �ow budget constraint

Q1tbt−1Π−1t − lt−1Π−1t −Tt +K = Q2tbt −Q1t lt

where K is any other central bank revenue net of operations cost

I An interest-rate feedback rule

βQ−11t =

(Πt

Π

)φπ

exp(εIt)

where φπ≥ 0

I Surprise and news shock

εIt = ρεIt−1 + exp(σ)εt

εIt = ρεIt−1 + exp(σ)εt−k

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Monetary policy

I Transfer to the treasury rules

T bt −

T

2= ψbTβ (bt−1−b) , T l

t −T

2=−ψlT (lt−1− l)

I Total transfer to the Treasury (Tt = T bt +T l

t )

Tt −T = ψbTβ (bt−1−b)−ψlT (lt−1− l)

I Baseline/speci�c case

Tt −T = ψT [β (bt−1−b)− (lt−1− l)]

I Gross position constant over time (T bt =T l

t )

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Fiscal policy

I No govt spending for simplicity

I Treasury turns over all central bank remittances to the household

I Treasury has zero holdings of reserves and long-term bonds

I So, very simple �scal policy

Tt = τt

LTt = 0, BTt = 0

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Market clearing and de�nitions

I Market clearing

yt(i) = ct(i) +d

(Pt(i)

Pt−1(i)

)bt −bHt = bTt = 0, lHt − lt = lTt = 0

I De�nitions (similar to the simple model)

RN,t ≡Q1t

Q2t− 1

Q1t

bN,t−1 ≡ [β (bt−1−b)− (lt−1− l)]

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Policy regimes and functional forms

I Policy rules

βQ−11t =

(Πt

Π

)φπ

exp(εIt)

Tt −T = ψT [β (bt−1−b)− (lt−1− l)]

I Policy regimesI Balance sheet unconstrained regime: φπ > 1; su�ciently large ψTI Balance sheet constrained regime: φπ < 1; small ψT

I Functional forms

U (ct ,ht) = logCt −Aht , yt = ht

d (Πt) =κ

2(Πt −1)2

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Calibration and simulation

I Baseline parameterization

Table: Parameterization of the model

Parameter Value Parameter Value

b 1 φπ 1.05; 0.95κ 150 ψT 0.012; 0.009T 0.1 ν 7β 0.99 ρ 0

I Fully non-linear deterministic simulationI Economy starts in the non-stochastic steady-state and then transitionsback to it in the long-run

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Balance sheet unconstrained central bankImpulse responses to a surprise monetary policy shock

0 4 8 12 16 200

0.2

0.4

0.6

0.8

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Short-term Interest Rate(Q−1

1t , %)

0 4 8 12 16 20

-0.03

-0.02

-0.01

0

Inflation(Πt, %)

0 4 8 12 16 20

-0.8

-0.6

-0.4

-0.2

0

Output(Yt, %)

0 4 8 12 16 20Quarters

-0.8

-0.6

-0.4

-0.2

0

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Net Asset Position(bN,t, % point)

0 4 8 12 16 20Quarters

-0.8

-0.6

-0.4

-0.2

0

Net Interest Income(RN,t, % point)

0 4 8 12 16 20Quarters

-0.01

-0.008

-0.006

-0.004

-0.002

0

Transfers to Treasury(Tt, % point)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Balance sheet constrained central bankImpulse responses to a surprise monetary policy shock

0 4 8 12 16 20

-0.6

-0.4

-0.2

0

0.2

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Short-term Interest Rate(Q−1

1t , %)

0 4 8 12 16 20-0.8

-0.7

-0.6

-0.5

Inflation(Πt, %)

0 4 8 12 16 20

-1

-0.8

-0.6

-0.4

Output(Yt, %)

0 4 8 12 16 20Quarters

-0.8

-0.6

-0.4

-0.2

0

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Net Asset Position(bN,t, % point)

0 4 8 12 16 20Quarters

-0.8

-0.6

-0.4

-0.2

0

Net Interest Income(RN,t, % point)

0 4 8 12 16 20Quarters

-8

-6

-4

-2

0×10-3

Transfers to Treasury(Tt, % point)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Balance sheet constrained central bank

I Positive interest rate shock leads to a decline in net interest income

I Balance sheet considerations mean net interest income rises in future

I Net interest income increase requires a fall in future of the short-terminterest rate and a slow transition back

I The short-term interest rate is below steady-state, but this leads to afall in in�ation in this regime (positively correlated!)

I Output falls on impact and throughout the transition (sticky prices)I Real e�ects stronger and more persistent (paradoxical?)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

ComparisonReal interest rate across the two regimes

I Correlation between nominal and real interest rate di�erent

I Nominal rate below while real rate above steady-state when thecentral bank is balance sheet constrained

0 4 8 12Quarters

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Short-term Interest Rate (Q−11t , %)

0 4 8 12Quarters

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Real Interest Rate (Q−11t /EtΠt+1, %)

Balance SheetUnconstrained Central BankBalance SheetConstrained Central Bank

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Balance sheet unconstrained central bankImpulse responses to an anticipated monetary policy shock

0 10 20 30 40

-0.4

-0.2

0

0.2

New

s Sh

ock

toSh

ort-

term

Int

eres

t Rat

eShort-term Interest Rate

(Q−11t , %)

0 10 20 30 400

0.05

0.1

0.15

0.2

Inflation(Πt, %)

0 10 20 30 400

0.1

0.2

0.3

0.4

Output(Yt, %)

0 10 20 30 40Quarters

-0.6

-0.4

-0.2

0

New

s Sh

ock

toSh

ort-

term

Int

eres

t Rat

e

Net Asset Position(bN,t, % point)

0 10 20 30 40Quarters

-0.4

-0.2

0

0.2

0.4

Net Interest Income(RN,t, % point)

0 10 20 30 40Quarters

-8

-6

-4

-2

0×10-3

Transfers to Treasury(Tt, % point)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Balance sheet constrained central bankImpulse responses to an anticipated monetary policy shock

0 10 20 30 40-0.6

-0.4

-0.2

0

New

s Sh

ock

toSh

ort-

term

Int

eres

t Rat

eShort-term Interest Rate

(Q−11t , %)

0 10 20 30 40

-0.1

-0.05

0

0.05

Inflation(Πt, %)

0 10 20 30 40-0.1

0

0.1

0.2

0.3

Output(Yt, %)

0 10 20 30 40Quarters

-0.6

-0.4

-0.2

0

New

s Sh

ock

toSh

ort-

term

Int

eres

t Rat

e

Net Asset Position(bN,t, % point)

0 10 20 30 40Quarters

-0.4

-0.2

0

0.2

0.4

Net Interest Income(RN,t, % point)

0 10 20 30 40Quarters

-5

-4

-3

-2

-1

0×10-3

Transfers to Treasury(Tt, % point)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Balance sheet constrained central bank

I There is an increase in in�ation and output today

I But in�ation falls in future and after the shock is realized

I Net interest income cannot go back immediately to steady-state afterthe shock is realized

I Short-term interest rate stays below steady-state after the shock

I Positive correlation between short-term interest rate and in�ationI In�ation falls after the shock is realizedI Output falls because of sticky prices

I Incentive to keep short-term interest rate low with maturity mismatchis the mechanism for QE in Bhattarai, Eggertsson, and Gafarov(2016), but equilibrium here is di�erent

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

ComparisonNet interest income across the two regimes

0 10 20 30 40Quarters

-0.06

-0.04

-0.02

0

0.02

0.04

0.06N

ews

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Net Interest Income (RN,t, % point)

Balance SheetUnconstrained Central BankBalance SheetConstrained Central Bank

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

ComparisonOutput across the two regimes

0 10 20 30 40Quarters

-0.1

0

0.1

0.2

0.3

0.4

New

s Sh

ock

toSh

ort-

term

Int

eres

t Rat

e

Output (Yt, %)

Balance SheetUnconstrained Central BankBalance SheetConstrained Central Bank

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

ComparisonIn�ation across the two regimes

0 10 20 30 40Quarters

-0.1

-0.05

0

0.05

0.1

0.15

0.2

New

s Sh

ock

toSh

ort-

term

Int

eres

t Rat

e

Inflation (Πt, %)

Balance SheetUnconstrained Central BankBalance SheetConstrained Central Bank

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

ComparisonReal interest rate across the two regimes

I Correlation between nominal and real interest rate di�erent

I Nominal rate below while real rate above steady-state when thecentral bank is balance sheet constrained

0 10 20 30 40Quarters

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

New

s Sh

ock

toSh

ort-

term

Int

eres

t Rat

e

Short-term Interest Rate (Q−1t , %)

0 10 20 30 40Quarters

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06Real Interest Rate (Q−1

1t /EtΠt+1, %)

Balance SheetUnconstrained Central BankBalance SheetConstrained Central Bank

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Forward guidance puzzle

I The standard sticky price model leads to large output/in�ation e�ectsof forward guidance policy (even very far out in the future)

I This has been dubbed the forward guidance puzzle

I Literature has emphasized the in�nite horizon and forward lookingbehavior of �rms/households as key reasons behind this result

I Proposed resolutionsI Finite life-times (Del Negro, Giannoni, and Patterson (2015))I Sticky information instead of sticky prices (Kiley (2016))I Borrowing constraints (Mckay, Nakamura, and Steinsson (2016))

I Model here: in�nite horizon, sticky prices, no borrowing constraintsbut a central bank constrained by balance sheet considerations

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Forward guidance puzzleComparison with Mckay, Nakamura, and Steinsson (2016) (Output)

0 10 20 30 40Quarters

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6Output (Yt, %)

Unconstrained CBConstrained CB

0 10 20 30 40Quarters

0

0.05

0.1

0.15

0.2

0.25

0.3McKay, Nakamura and Steinsson(2016)

Complete MarketsIncomplete Markets

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Forward guidance puzzleComparison with Mckay, Nakamura, and Steinsson (2016) (In�ation)

0 10 20 30 40Quarters

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Inflation (Πt, %)

Unconstrained CBConstrained CB

0 10 20 30 40Quarters

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

McKay, Nakamura and Steinsson(2016)

Complete MarketsIncomplete Markets

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Forward guidance puzzleComparison with Mckay, Nakamura, and Steinsson (2016) (Output-FG Horizon)

0 4 8 12 16 20Horizon

0

0.2

0.4

0.6

0.8

1

1.2Initial Response of Output

Unconstrained CBConstrained CB

0 4 8 12 16 20Horizon

0

0.2

0.4

0.6

0.8

1

1.2McKay, Nakamura and Steinsson(2016)

Complete MarketsIncomplete Markets

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Extensions

I Open economy model with currency mismatchI Domestic currency liability and foreign currency asset

I Alternate model of balance sheet constrained central bankI A lower bound on transfers to the Treasury that binds endogenouslyI Central bank regime switches endogenously

I A binding zero lower bound on the nominal rate

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Open economy model

I Model of currency mismatch

I Nominal central bank �ow budget constraint

StB∗t−1−Lt−1−Mt−1−PtTt = StQB∗tB

∗t −QLtLt −Mt

where St is the nominal exchange rate

I Balance sheet variablesI Lt : one-period domestic currency liabilities with QL,t its priceI Bt : one-period foreign currency assets with QB∗t its price

I Monetary/�scal policy interaction variableI Tt : central bank transfer to the Treasury

I Conventional monetary policy instrumentI QL,t : one-period domestic bond price

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Open economy model

I Real �ow budget constraint

ςtb∗t−1Π∗−1t − lt−1Π−1t −mt−1Π−1t −Tt = ςtQB∗tb

∗t −QLt lt −mt

where ςt ≡ StP∗tPt

is the real exchange rate

I Complete market asset-pricing and PPP

I Approximate the budget constraint and asset pricing conditions

I Budget constraint

bN,t =1

βbN,t−1−

1

βTt +b∗RN,t

where net interest income

RN,t ≡ St −βEt St+1

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Open economy model

I PV form

bN,t−1 =∞

∑t=0

βtTt −βb∗

∞

∑t=0

βtRN,t

where net interest income

RN,t ≡ St −βEt St+1

I When an open economy central bank is balance sheet constrained

I Increase in RN,t today leads to a decrease in futureI Exchange rate path in future gets constrainedI Unpleasant central bank balance sheet arithmetic in an open economy

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Alternate model of balance sheet constraint

I A lower bound on central bank transfers: Tt −T ≥−χ

I If this bound not reached, then

βQ−11,t =

(Πt

Π

)φπ

exp(εIt), Tt −T = ψT [β (bt−1−b)− (lt−1− l)]

where φπ> 1 and ψT su�ciently large

I If this bound is reached, then

βQ−11,t =

(Πt

Π

)φπ

exp(εIt), Tt −T =−χ

where φπ< 1

I Whether and how long this constraint binds determined endogenously

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Alternate model of balance sheet constraintSurprise monetary policy shock

0 4 8 12 160

0.2

0.4

0.6

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Short-term Interest Rate(Q−1

1t , %)

0 4 8 12 16-15

-10

-5

0×10-4

0 4 8 12 16

-0.4

-0.3

-0.2

-0.1

0

Inflation(Πt, %)

0 4 8 12 16-0.8

-0.6

-0.4

-0.2

0

Output(Yt, %)

Balance SheetUnconstrained CBBalance SheetConstrained CB

0 4 8 12 16Quarters

-0.6

-0.4

-0.2

0

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Net Asset Position(bN,t, % point)

0 4 8 12 16Quarters

-0.6

-0.4

-0.2

0

Net Interest Income(RN,t, % point)

0 4 8 12 16

0

2

4

×10-4

0 10 20 30 40 50 60Quarters

-0.02

-0.015

-0.01

-0.005

0

Transfers to Treasury(Tt, % point)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Alternate model of balance sheet constraintAnticipated monetary policy shock

0 4 8 12 16

-0.5

0

0.5

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Short-term Interest Rate(Q−1

1t , %)

0 4 8 12 16-15

-10

-5

0×10-4

0 4 8 12 16

0

0.2

0.4

0.6

Inflation(Πt, %)

0 4 8 12 16

0

0.2

0.4

0.6

Output(Yt, %)

0 4 8 12 16Quarters

-1.5

-1

-0.5

0

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Net Asset Position(bN,t, % point)

0 4 8 12 16Quarters

-1

-0.5

0

0.5

1

Net Interest Income(RN,t, % point)

0 4 8 12 16

0

2

4

×10-4

0 10 20 30 40 50 60Quarters

-0.04

-0.03

-0.02

-0.01

0

Transfers to Treasury(Tt, % point)

Balance SheetUnconstrained CBBalance SheetConstrained CB

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Zero lower bound

I How do the two central bank models compare at the ZLB?

I Introduce a preference/demand shock in the model

I But the comparison not straightforward at allI For a negative demand shock, nominal rate falls slightly initially for thebalance sheet constrained central bank, but increases next period

I ZLB can bind in future for a positive demand shock for the balancesheet constrained central bank

I As emphasized before, nominal and real rate correlation di�erent alongthe transition across the two regimes

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Negative demand shockPositive interest rates

0 4 8 12 16 20

-0.15

-0.1

-0.05

0

0.05

Neg

ativ

e D

eman

d Sh

ock

Short-term Interest Rate(Q−1

1t , %)

0 4 8 12 16 20-0.15

-0.1

-0.05

0

0.05

Inflation(Πt, %)

0 4 8 12 16 20-0.8

-0.6

-0.4

-0.2

0

Output(Yt, %)

Balance SheetUnconstrained CBBalance SheetConstrained CB

0 4 8 12 16 20Quarters

0

0.05

0.1

0.15

Neg

ativ

e D

eman

d Sh

ock

Net Asset Position(bN,t, % point)

0 4 8 12 16 20Quarters

0

0.01

0.02

0.03

Net Interest Income(RN,t, % point)

0 4 8 12 16 20Quarters

0

5

10

15

×10-4

Transfers to Treasury(Tt, % point)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Negative demand shockZero lower bound

0 4 8 12 16 20-1

0

1

2

Neg

ativ

e D

eman

d Sh

ock

Short-term Interest Rate(Q−1

1t , %)

0 4 8 12 16 20

-10

-5

0

Inflation(Πt, %)

0 4 8 12 16 20

-60

-40

-20

0

Output(Yt, %)

Balance SheetUnconstrained CBBalance SheetConstrained CB

0 4 8 12 16 20Quarters

0

1

2

3

Neg

ativ

e D

eman

d Sh

ock

Net Asset Position(bN,t, % point)

0 4 8 12 16 20Quarters

0

0.2

0.4

0.6

Net Interest Income(RN,t, % point)

0 4 8 12 16 20Quarters

0

0.005

0.01

0.015

0.02

0.025

Transfers to Treasury(Tt, % point)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Sensitivity analysis

I Di�erent interest rate and transfer policy rule parameters

I More general central bank transfer ruleI Tt −T = ψbTβ (bt−1−b)−ψlT (lt−1− l)I ψbT = 0.009 and ψlT = 0.005

I Stochastic solution method (second-order perturbation)I Results not speci�c to a deterministic solution methodI In principle, incorporates a term premium

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Interest rate rule parameterBalance sheet constrained central bank

0 4 8 12 16

-0.6

-0.4

-0.2

0

0.2

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Short-term Interest Rate(Q−1

1t , %)

0 4 8 12 16

-0.9

-0.8

-0.7

-0.6

-0.5

Inflation(Πt, %)

0 4 8 12 16

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

Output(Yt, %)

0 4 8 12 16Quarters

-0.8

-0.6

-0.4

-0.2

0

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Net Asset Position(bN,t, % point)

0 4 8 12 16Quarters

-0.8

-0.6

-0.4

-0.2

0

Net Interest Income(RN,t, % point)

φπ = 0.90

φπ = 0.95

φπ = 0.97

0 4 8 12 16Quarters

-8

-6

-4

-2

0×10-3

Transfers to Treasury(Tt, % point)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Transfer rule parameterBalance sheet constrained central bank

0 4 8 12 16-0.8

-0.6

-0.4

-0.2

0

0.2

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Short-term Interest Rate(Q−1

1t , %)

0 4 8 12 16

-0.9

-0.8

-0.7

-0.6

-0.5

Inflation(Πt, %)

0 4 8 12 16

-1

-0.8

-0.6

-0.4

Output(Yt, %)

0 4 8 12 16Quarters

-0.8

-0.6

-0.4

-0.2

0

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Net Asset Position(bN,t, % point)

0 4 8 12 16Quarters

-0.8

-0.6

-0.4

-0.2

0

Net Interest Income(RN,t, % point)

ψT = 0.0095

ψT = 0.0090

ψT = 0.0050

0 4 8 12 16Quarters

-8

-6

-4

-2

×10-3

Transfers to Treasury(Tt, % point)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

General central bank transfer ruleBalance sheet constrained central bank

0 4 8 12 16 20

-0.6

-0.4

-0.2

0

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Short-term Interest Rate(Q−1

1t , %)

0 4 8 12 16 20

-0.8

-0.7

-0.6

-0.5

Inflation(Πt, %)

0 4 8 12 16 20

-1

-0.8

-0.6

-0.4

Output(Yt, %)

0 4 8 12 16 20Quarters

-0.8

-0.6

-0.4

-0.2

0

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Net Asset Position(bN,t, % point)

0 4 8 12 16 20Quarters

-0.8

-0.6

-0.4

-0.2

0

Net Interest Income(RN,t, % point)

0 4 8 12 16 20Quarters

-6

-4

-2

0×10-3

Transfers to Treasury(Tt, % point)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Stochastic solution methodBalance sheet constrained central bank

0 4 8 12 16 20

-0.6

-0.4

-0.2

0

0.2

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Short-term Interest Rate(Q−1

1t , %)

0 4 8 12 16 20

-0.7

-0.6

-0.5

-0.4

Inflation(Πt, %)

0 4 8 12 16 20

-1.6

-1.4

-1.2

-1

-0.8

-0.6

Output(Yt, %)

0 4 8 12 16 20Quarters

-0.8

-0.6

-0.4

-0.2

0

Shoc

k to

Shor

t-te

rm I

nter

est R

ate

Net Asset Position(bN,t, % point)

0 4 8 12 16 20Quarters

-0.8

-0.6

-0.4

-0.2

0

Net Interest Income(RN,t, % point)

0 4 8 12 16 20Quarters

-8

-6

-4

-2

0×10-3

Transfers to Treasury(Tt, % point)

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic

Introduction Balance Sheet Data Simple Model GE Model Extensions Conclusion

Conclusion

I Whether or not the central bank faces a balance sheet constraint canalter standard results on monetary policy

I Key driver is if the path of remittances to Treasury is constrainedwhen central bank balance sheet has maturity (or currency) mismatch

I Future path of monetary policy instrument gets a�ected non-triviallyunder central bank balance sheet constraints

I Signi�cantly alters the transmission of monetary policy shock (bothsurprise and anticipated)

I Changes the correlation of the nominal and real rate

Saroj Bhattarai (UT-Austin) Central Bank Balance Sheet Arithmetic