Welfare-Enhancing Distributional Eects of Central Bank Asset - - PowerPoint PPT Presentation

Welfare-Enhancing Distributional E¤ects of Central Bank Asset Purchases

Andreas Schabert University of Cologne November, 2017

2 I INTRODUCTION II THE MODEL III WELFARE ENHANCING ASSET PURCHASES IV STATE CONTINGENCY V CONCLUSION

INTRODUCTION

3 Central bank asset purchases Should central banks (CBs) intervene in secondary markets for private debt securities? – Large scale purchases of debt securities were added into the CB instrument set – Several studies report gains of unconventional policies in times of …nancial stress Recent experiences with asset purchases suggest measurable asset price e¤ects – Asset purchase reduced yields on long-term treasuries (De Fiore et al., 2016) – MBS purchases reduced yields and mortgage rates (Hancock and Passmore, 2014)

INTRODUCTION

4 Redistributive e¤ects of asset purchases Is there a useful role for asset purchases (AP) even in tranquil times and o¤ the ZLB? – Even if they are non-neutral, they might be equivalent to conventional policies This paper – AP drive a wedge between the e¤ective rates for lenders and borrowers – Not possible by conventional instruments (interest rates or in‡ation target) – They can induce a redistribution of funds from lenders to borrowers

INTRODUCTION

5 Welfare enhancing role of asset purchases CB purchases of assets distort market prices and might raise or lower e¢ciency – Even if borrowers are constrained, redistribution can reduce social welfare Novel insights – Financial constraint induces constrained ine¢ciency due to externalities – AP can serve as a Pigouvian subsidy and enhance welfare even further – State contingent asset purchases should be countercyclical

INTRODUCTION

6 The framework Endowment economy with idiosyncratic shocks and limited contract enforcement – Positive feedback loop between collateral demand, prices, and borrowing capacity Fiat money as a medium of exchange – Fully backed by eligible assets (treasuries or collateralized debt) – Conventional monetary policy is neutral

INTRODUCTION

7 Related literature Bene…cial unconventional monetary policies under stressed …nancial markets – Curdia and Woodford (2011), Gertler and Karadi (2011), Chen et al. (2012), Del Negro et al. (2016), Woodford (2016) and others Redistributive e¤ects of conventional monetary policy – Akyol (2004), Berentsen et al., (2005), Algan and Ragot (2010), Lippi et al. (2015), Auclert (2016), Garriga et al. (2016) and others Constrained ine¢ciency under pecuniary externalities and …nancial constraints – Lorenzoni (2008), Bianchi (2011), Stein (2012), Bianchi and Mendoza (2017), Jeanne and Korinek (2016), Davila and Korinek (2017) and others

8 I INTRODUCTION II THE MODEL III WELFARE ENHANCING ASSET PURCHASES IV STATE CONTINGENCY V CONCLUSION

THE MODEL

9 Overview Households face idiosyncratic shocks, hold treasuries, money, and durables (housing) – They rely on …at money for purchases of non-durables – They can get money from the CB against eligible assets (treasuries) A household with a relatively high valuation of non-durables – can borrow intraperiod from other households against collateral (durables) Central bank buys treasuries and can further purchase collateralized debt – Treasury issues short-term debt in an ad-hoc way

THE MODEL

10 Timing Beginning of the period – Aggregate shocks are realized – Money is supplied against treasuries – Idiosyncratic preference shocks are realized – Loans are originated and might be purchased by the central bank – Household members purchase goods with …at money – Loans are repaid, repos are settled, and assets are traded End of the period

THE MODEL

11 Households I/III In…nitely lived households i 2 [0; 1] with identical initial wealth and endowment – Utility depends on consumption ci;t and housing hi;t ui;t = u(i; ci;t; hi;t) – i.i.d. preference shocks i 2 fb, lg with equal probabilities and l < b They can get money Ii;t against eligible assets discounted with the policy rate Rm

t

Ii;t B

t Bi;t1=Rm t

where Bi;t1 denotes treasuries and B

t the fraction of purchased treasuries.

THE MODEL

12 Households II/III Agents drawing b borrow, Li;t > 0, at the loan rate RL

t against collateral

Li;t ztPtqthi;t; where zt 2 (0; 1) is a liquidation value, qt the housing price, and Pt the price level. CB might o¤er purchases of a fraction t of secured loans Ll;t = Lb;t IL

l;t t Ll;t=Rm t :

Lenders are willing to sell secured loans for above market prices Rm

t RL t

Households rely on money for purchases of consumption goods (for b and l) Ptci;t Ii;t + IL

i;t + MH i;t1 Li;t=RL t :

THE MODEL

13 Households III/III Households maximize welfare taking all constraints into account – Borrowers’ loan demand satis…es (with the collateral constraint multiplier i;t) 1 RL

t

= Et

h

u0(i; ci;t+1)=t+1

i

u0(i; ci;t) + i;t u0(i; ci;t) – Lenders’ loan supply satis…es 1 RL

t

= 1 t 1 tRL

t =Rm t

Et

h

u0(i; ci;t+1)=t+1

i

u0(i; ci;t) The wedge

1t 1tRL

t =Rm t

exceeds one for Rm

t < RL t and a positive fraction t > 0

– It increases with a larger fraction t and a larger price discount RL

t =Rm t .

THE MODEL

14 Monetary policy The central bank sets the price of money in terms of eligible assets Rm

t 1

– decides how many assets are purchased t 2 [0; 1] and B

t 2 (0; 1]

– supplies money outright and temporarily, MR

t = tMH t ,

– and transfers its interest earnings leading to the balance sheet Bc

t = MH t :

CB can control both prices and money supply under money rationing (Schabert, 2015) Rm

t < RL t

THE MODEL

15 Government The government issues bonds and has access to lump-sum taxes/transfers t – Supply of short-term government bonds is speci…ed in an ad-hoc way ( > ): BT

t = BT t1

– This policy does not support the implementation of …rst best, which satis…es uc(b; c

b;t) = uc(l; c l;t); and h b;t = h l;t:

16 I INTRODUCTION II THE MODEL III WELFARE ENHANCING ASSET PURCHASES IV STATE CONTINGENCY V CONCLUSION

WELFARE ENHANCING ASSET PURCHASES

17 Simplifying assumptions Assumptions

• 1. Instantaneous utility of households satis…es

u(i; ci;t; hi;t) = i(ci;t (1=2)c2

i;t) + (hi;t (1=2)h2 i;t),

where @u=@ci;t = u0(i; ci;t) > 0 and @u=@hi;t = u0(hi;t) > 0.

• 2. Agents will hold money equal to the amount of planned nominal consumption

expenditures even when the multiplier on the cash-in-advance constraint equals zero.

• 3. The ratio (b l)=z is su¢ciently large such that the borrowing constraint is

binding for all agents drawing b.

WELFARE ENHANCING ASSET PURCHASES

18 Aggregation Under Assumptions 1-3, a competitive equilibrium in terms of a representative bor- rower and a representative lender under a conventional monetary policy regime is a set of sequences fcb;t; cl;t; hb;t, qt, tg1

t=0 satisfying

ucl;t = Et

h

0:5(ucl;t+1 + ucb;t+1)

n

RL

t =t+1

• i

;

n

RL

t =qt

• (2hb;t h)=z = ucb;t Et[0:5(ucl;t+1 + ucb;t+1)

n

RL

t =t+1

• ];

ucl;t

n

qt=RL

t

• = uhl + Et[ucl;t+1

n

qt+1=RL

t+1

• ];

cb;t cl;t = zhb;t2

n

qt=RL

t

• ;

yt = cb;t + cl;t; and RL

t = Rm t , for fytg1 t=0 and a sequence fRm t 1g1 t=0 set by the central bank.

WELFARE ENHANCING ASSET PURCHASES

19 Neutrality of conventional monetary policy Under a binding borrowing constraint consumption and housing satis…es b;t = [ucb;t ucl;t]=RL

t =

• 2hb;t h
• =(zqt) > 0;

(1) Corollary 2 Under a conventional monetary policy regime, changes in the monetary policy rate do not a¤ect the equilibrium allocation, while the housing price and the in‡ation rate increase with the nominal interest rate.

WELFARE ENHANCING ASSET PURCHASES

20 A pecuniary externality When there is no aggregate risk, the relative price of collateral q=RL satis…es q RL = uhl(h hb) (1 )ucl(y cb) – The relative price is increasing (decreasing) in borrowers’ housing (consumption). – A Pigouvian tax/subsidy on debt issuance can address the externality RL

t =t+1

1L

t

Proposition 1 The implementation of a constrained e¢cient allocation of the rep- resentative agents economy without aggregate risk requires a subsidy on borrowing, L < 0, if but not only if z=(1 ) 1. Compared to the laissez-faire case (L = 0), the Pigouvian subsidy raises borrowers’ consumption and housing as well as the real interest rate RL=, which is associated with a decline in lenders’ con- sumption and housing.

WELFARE ENHANCING ASSET PURCHASES

21 Equilibrium under asset purchases A competitive equilibrium without aggregate risk and a price discount s = RL=Rm > 1 is a set fcb; cl; hbg satisfying y = cl + cb,

1

1 s

• ucb = ucl

@1 + 1

z uhl uhb uhl

1 A ;

cb cl = hb z 1 uhl ucl

• "

(1 ) (2 s) (1 s)

#

; The corresponding set fcl; cb; hbg under the optimal Pigouvian subsidy e L satis…es

h

1 e Li ucb = ucl

@1 + 1

z uhl uhb uhl

1 A ;

cb cl = hb z 1 uhl ucl [2] ; and y = cl + cb.

WELFARE ENHANCING ASSET PURCHASES

22 Welfare enhancing asset purchases The instruments and s can be set to replicate the optimal subsidy e L. Proposition 2 Suppose that money supply is rationed and z 1 . Then, the constrained e¢cient allocation under the Pigouvian subsidy can be implemented by the central bank via asset purchases. For (1)(2s)

(1s)

> 2, welfare dominating allocations can even be implemented. Proposition 3 Suppose that money supply is rationed and there is no aggregate risk. Then, the …rst best equilibrium cannot be implemented, while the central bank can implement allocations via asset purchases that welfare-dominate allocations that are implementable under a Pigouvian subsidy.

WELFARE ENHANCING ASSET PURCHASES

23 Numerical results Numerical version with CRRA preferences – End-of-period wealth redistribution to facilitate aggregation – Competitive equilibrium solely changes with regard to the marginal utilities – All results are qualitatively unchanged Parametrization with standard values taken from the literature and three targets – MBS yields, installment loans share, cross sectional st.dev. of consumption

WELFARE ENHANCING ASSET PURCHASES

24

1 1.05 1.1 1.15 1.2 0.2 0.4 0.6

• 30
• 20
• 10

10 1 1.05 1.1 1.15 1.2 0.2 0.4 0.6

• 20

20 40 1 1.05 1.1 1.15 1.2 0.2 0.4 0.6

• 50

50 100 150 1 1.05 1.1 1.15 1.2 0.2 0.4 0.6

• 5

5 10

E¤ects of and s for = 1:07 (in % deviations from laissez faire values)

WELFARE ENHANCING ASSET PURCHASES

25

1 1.05 1.1 1.15 1.2 0.2 0.4 0.6

• 1

1 2 3 1 1.05 1.1 1.15 1.2 0.2 0.4 0.6

• 20

20 40 1 1.05 1.1 1.15 1.2 0.2 0.4 0.6

• 30
• 20
• 10

10 1 1.05 1.1 1.15 1.2 0.2 0.4 0.6

• 0.5

0.5 1

E¤ects of and s for = 1:07 (in % deviations from laissez faire values)

WELFARE ENHANCING ASSET PURCHASES

26

1 1.5 2 2.5 3 3.5 4 0.2 0.4 0.6 0.8 1 z=0.55 z=0.45 CEA z=0.55 CEA z=0.45 1 1.5 2 2.5 3 3.5 4 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 1 1.5 2 2.5 3 3.5 4 4.5 1.3 1.32 1.34 1.36 1.38 1 1.5 2 2.5 3 3.5 4 0.7254 0.7256 0.7258 0.726 0.7262 0.7264 0.7266

Asset purchases and the constrained e¢cient allocation for variations in s

WELFARE ENHANCING ASSET PURCHASES

27

1 1.5 2 2.5 3 3.5 4 0.91 0.915 0.92 0.925 0.93 1 1.5 2 2.5 3 3.5 4 0.5 0.6 0.7 0.8 0.9 1 1.5 2 2.5 3 3.5 4 0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 1 1.5 2 2.5 3 3.5 4 0.8 0.9 1 1.1 1.2 1.3 1.4

Asset purchases and the constrained e¢cient allocation for variations in s

28 I INTRODUCTION II THE MODEL III WELFARE ENHANCING ASSET PURCHASES IV STATE CONTINGENCY V CONCLUSION

STATE CONTINGENCY

29 Introducing aggregate risk We add a random process for aggregate income (estimated with US data) Asset purchases are adjusted in a state contingent way for a …xed s – The mean is identical to a constant Pigouvian subsidy Borrowing is supported in response to adverse shocks – E¤ective liquidation value e zt = z

2 (1)(2s) (1s)

is increased – Borrowers’ real rate is reduced, lenders’ real rate is increased Corresponding results for stochastic realizations of the liquidation value zt:

STATE CONTINGENCY

30

1 2 3 4 5 6 7 8 0.05 0.1 0.15 0.2 1 2 3 4 5 6 7 8

• 2.5
• 2
• 1.5
• 1
• 0.5

Optimal asset purchases Constant Pigouvian subsidy 1 2 3 4 5 6 7 8

• 2.5
• 2
• 1.5
• 1
• 0.5

1 2 3 4 5 6 7 8

• 2
• 1.5
• 1
• 0.5

Responses to a negative aggregate endowment shock

STATE CONTINGENCY

31

1 2 3 4 5 6 7 8

• 1.5
• 1
• 0.5

1 2 3 4 5 6 7 8 0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 0.2 0.4 0.6 0.8 1 1.2 1.4 1 2 3 4 5 6 7 8 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Responses to a negative aggregate endowment shock

32 I INTRODUCTION II THE MODEL III WELFARE ENHANCING ASSET PURCHASES IV STATE CONTINGENCY V CONCLUSION

CONCLUSION

33 Asset purchases exert e¤ects distinct from conventional monetary policy – Useful role even in non-crisis times – Price e¤ects can be used as a Pigouvian subsidy – Borrowing can be stimulated even further Asset purchases can address ine¢ciencies from …nancial frictions – Support prudential (ex-ante) policies

34 ADDITIONAL SLIDES

ADDITIONAL SLIDES

35

1 2 3 4 5 6 7 8 0.02 0.04 0.06 0.08 0.1 0.12 0.14 1 2 3 4 5 6 7 8

• 0.15
• 0.1
• 0.05

0.05 Optimal asset purchases Constant Pigouvian subsidy 1 2 3 4 5 6 7 8

• 0.1

0.1 0.2 0.3 1 2 3 4 5 6 7 8 0.2 0.4 0.6 0.8 1 1.2 1.4

Responses to a minus one st.dev. liquidation value shock

ADDITIONAL SLIDES

36

1 2 3 4 5 6 7 8

• 0.8
• 0.6
• 0.4
• 0.2

1 2 3 4 5 6 7 8

• 1.4
• 1.2
• 1
• 0.8
• 0.6
• 0.4
• 0.2

1 2 3 4 5 6 7

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.1 0.2 1 2 3 4 5 6 7 8 0.2 0.4 0.6 0.8 1 1.2 1.4

Responses to a minus one st.dev. liquidation value shock