Optimal monetary policy, asset purchases, and credit market - - PowerPoint PPT Presentation

Optimal monetary policy, asset purchases, and credit market frictions

Andreas Schabert, University of Cologne June, 2014

2 I INTRODUCTION II THE MODEL III CONSTRAINED BORROWING AND MONETARY POLICY IV OPTIMAL POLICY AND ASSET PURCHASES V CONCLUSION

INTRODUCTION

3 This paper How do …nancial market frictions matter for the conduct of monetary policy? – Trade-o¤ of a welfare maximizing central bank (CB) Is there a role for central bank purchases (not creation) of loans? – A CB asset exchange is typically irrelevant Main idea – CB asset purchases can matter when money supply is rationed

INTRODUCTION

4 The model A sticky price model where money is essential and private agents borrow/lend – To facilitate aggregation, we consider ex-ante identical agents (Shi, 1997) Household members draw preference shocks – High valuation of consumption ! borrowing money from other members Financial market friction – Private debt contracts are not perfectly enforceable – Loans secured by pledgeable assets (Kiyotaki and Moore, 1997)

INTRODUCTION

5 Monetary policy Central bank supplies money against eligible assets – Money supply is fully backed (e.g. by treasury securities) – Central bank sets the price of money in terms of eligible assets When the policy rate equals the marginal valuation of money – Conventional regime where asset purchases are irrelevant When the policy rate is set below marginal valuation of money – Eligible asset are scare and quantitative instruments can matter

INTRODUCTION

6 Results Positive in‡ation rates are not desirable – Intraperiod loans: real debt burden cannot be reduced by higher in‡ation – In‡ation raises the loan rate and ampli…es the credit market friction Optimal monetary policy (without money rationing) – Under sticky prices: central bank mainly aims at stabilizing prices – When prices are more ‡exible, monetary policy eases the borrowing constraint CB can enhance welfare by purchasing asset at a favorable price

INTRODUCTION

7 Related studies Studies on optimal monetary policy under …nancial market frictions – Monacelli (2008): household borrowing constrained by collateral – De Fiore et al. (2011): optimal monetary policy under imperfect monitoring Studies on unconventional monetary policies – Curdia and Woodford (2011): direct central bank lending under costly banking – Gertler and Kiyotaki (2011): balance sheet constraint of …nancial intermediaries – Araújo et al. (2013): asset purchases without a speci…c role of currency

8 I INTRODUCTION II THE MODEL III CONSTRAINED BORROWING AND MONETARY POLICY IV OPTIMAL POLICY AND ASSET PURCHASES V CONCLUSION

THE MODEL

9 Timing Beginning of the period: Household members hold money, gov. bonds, and housing – Aggregate productivity shocks are realized – Money supplied against treasuries at policy rate – Idiosyncratic preference shocks are realized – Loans are originated and might be purchased by the central bank – Household members buy goods from …rms with money as means of payment – Borrowers repay loans and government bonds are issued End of the period

THE MODEL

10 Households I/IV In…nitely many households of measure one, each with members i 2 [0; 1] – household wealth equally distributed at the beginning of each period (Shi, 1997) – Utility depends on consumption ci;t, housing hi;t, labor ni;t u(i;t; ci;t; hi;t; ni;t) = i;t c1

i;t

1 1 + h1h

i;t

1 1 h n 1+

i;t

1 + ; – i.i.d. shocks i 2 fb, lg with equal probabilities and l < b End-of-period stock of housing hi;t might di¤er between both types of members – Supply of housing is …xed at h

THE MODEL

11 Households II/IV Money injections Ii;t against eligible assets discounted with the policy rate Rm

t

Ii;t B

t Bi;t1=Rm t ;

(1) Drawing b implies borrowing, partially constrained by collateral Lb;t ztPtqthb;t; where Lb;t < 0 (2) where zt is the liquidation value and qt the real price of the housing good. Lenders can re…nance secured loans Ll;t = Lb;t at the CB IL

l;t t Ll;t=Rm t

(3)

THE MODEL

12 Households III/IV Households rely on money for purchases of consumption goods Ptcl;t

• Il;t + IL

l;t + MH l;t1

h

(1 + ) Ll;t + Lr

l;t

i

=RL

t

Ptcb;t

• Ib;t + MH

b;t1

h

(1 + ) Lb;t + Lr

b;t

i

=RL

t

– Loans funded by proceeds of CB purchases Lr

l;t = Lr b;t Lr l;t=RL t

– Unsecured loans Ll;t and re…nanced loans Lr

l;t are not pledgeable

Lenders are willing to sell all secured loans to the CB if Rm

t < RL t

– Money supply constraint (1) and (3) are then binding (money rationing)

THE MODEL

13 Households IV/IV Maximizing E P1

t=0 tui;t s.t. money, goods, and asset market constraints

– Borrower’s credit demand is a¤ected by the borrowing constraint (b;t 0) 1 RL

t

= Et 0:5(bc

b;t+1 + lc l;t+1)

bc

b;t t+1

+ b;t bc

b;t (1 + )

; – Lender’s credit supply a¤ected by possible CB loan purchases 1 RL

t

= Et 0:5(bc

b;t+1 + lc l;t+1)

lc

l;t t+1

"

1 + t 1 + RL

t

Rm

t

1

!#

; – b;t = 0 and Rm

t = RL t lead to a standard consumption Euler equations.

THE MODEL

14 Firms Typical New Keynesian set-up – Identical intermediate goods producing …rms produces with labor and receive a constant subsidy that eliminates average mark-ups – Monopolistically competitive retailers buy intermediate goods and set prices like according to Calvo/Yun Price dispersion leads to short-run and long-run ine¢ciency – Minimized by price stability

THE MODEL

15 Central bank Central bank supplies money outright and temporarily, – sets the price of money in terms of eligible assets Rm

t 1

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

t 2 (0; 1]

– and transfers its interest earnings to the treasury Ptm

t = (1 1=Rt) Bc t + Rm t

• MH

t

MH

t1

• + (Rm

t 1)

• ML

t + MR t

• ;

leading to the end-of-period balance sheet Bc

t = MH t :

THE MODEL

16 Government Government issues one-period bonds, pays a subsidy at a constant rate, and – has access to lump-sum taxes/transfers t (BT

t =Rt) + Ptm t = BT t1 + Ptt + Ptp:

Supply of short-term government bonds is speci…ed in a simple way, BT

t = BT t1

where > and bond market clearing requires BT

t = Bt + Bc t.

THE MODEL

17 First best allocation Proposition 1: The …rst best allocation fc

b;t; c l;t; n b;t; n l;t,h b;t; h l;tg1 t=0 satis…es

b;t(c

b;t)

= l;t(c

l;t),

n

b;t

= n

l;t;

h

b;t

= h

l;t;

b(c

b;t) = [=(at)]0:5(n t)1+; h b;t +h l;t = h and c l;t +c b;t = at(n t).

Competitive equilibrium – Three frictions: borrowing constraint, cash vs. credit goods, and sticky prices

18 I INTRODUCTION II THE MODEL III CONSTRAINED BORROWING AND MONETARY POLICY IV OPTIMAL POLICY AND ASSET PURCHASES V CONCLUSION

CONSTRAINED BORROWING AND MONETARY POLICY

19 Long-run properties Suppose that money supply is not rationed (Rm = RL) – loan rate equals lender’s marginal rate of intertemporal substitution RL = (=)

• lc

l

=c where c = 0:5lc

l

+ 0:5bc

b

: – If the borrowing constraint is slack, b;t = 0, relative consumption satis…es lc

l

= bc

b

– If borrowing is constrained b;t > 0, relative consumption of the lender satis…es cl > (l=b)1= cb ! Tighter borrowing constraints lead to lower loan rates

CONSTRAINED BORROWING AND MONETARY POLICY

20

0.99 0.995 1 1.005 1.01 0.99 0.995 1 1.005 1.01 1.015 1.02 1.025 z= 0.8 z= 0.4 F r ictionles s 0.99 0.995 1 1.005 1.01 0.298 0.299 0.3 0.301 0.302 0.303 0.99 0.995 1 1.005 1.01 0.1725 0.173 0.1735 0.174 0.1745 0.175 0.99 0.995 1 1.005 1.01 0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.99 0.995 1 1.005 1.01 0.3225 0.323 0.3235 0.324 0.3245 0.325 0.3255 0.326 0.99 0.995 1 1.005 1.01

• 3.14
• 3.135
• 3.13
• 3.125
• 3.12

Steady state values for di¤erent in‡ation rates

21 I INTRODUCTION II THE MODEL III CONSTRAINED BORROWING AND MONETARY POLICY IV OPTIMAL POLICY AND ASSET PURCHASES V CONCLUSION

OPTIMAL POLICY AND ASSET PURCHASES

22 Flexible prices Proposition 2: A long-run e¢cient allocation can, in general, neither be imple- mented under rationed money supply nor under non-rationed money supply. E¢ciency would require the Friedman rule and a slack borrowing constraint – Under RL = 1, borrowing constraint will in general be binding – Money cannot be supplied in a rationed way, since Rm RL = 1 Under second best with (RL > 1) – Money rationing (Rm < RL) and purchasing loans can enhance welfare

OPTIMAL POLICY AND ASSET PURCHASES

23 Optimal monetary policy under sticky prices Central bank maximizes welfare under full commitment – Analysis restricted to time invariant policies (neglecting time inconsistency) Reasonable degree of price stickiness – Long-run in‡ation rate equals one (price stability) – Price stability even for tighter borrowing constraint (z=0.4) When prices are more ‡exible, – monetary policy eases the borrowing constraint

OPTIMAL POLICY AND ASSET PURCHASES

24 Steady state values under optimal monetary policy without money rationing

First best Benchmark More ‡exible prices Tighter

• borrow. constraint

Consumption of the borrower 0.3018 0.3009 0.3010 0.3003 Consumption of the lender 0.1742 0.1739 0.1739 0.1744 Borrower’s housing share 0.5 0.5334 0.5333 0.6369 Working time 0.3248 0.3235 0.3237 0.3233 Loan rate

–

1.0091 1.0007 1.0044 In‡ation rate

–

1 0.9982 1 Representative agent utility –3.12078 –3.12086 –3.12085 –3.12145

OPTIMAL POLICY AND ASSET PURCHASES

25

1 2 3 4 5 6 7 8 9 10 0.05 0.1 0.15 0.2 0.25 0.3 0.35 1 2 3 4 5 6 7 8 9 10

• 0.4
• 0.35
• 0.3
• 0.25
• 0.2
• 0.15
• 0.1
• 0.05

1 2 3 4 5 6 7 8 9 10

• 0.4
• 0.35
• 0.3
• 0.25
• 0.2
• 0.15
• 0.1
• 0.05

φ=0.7 φ=0.1 First best 1 2 3 4 5 6 7 8 9 10 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 1 2 3 4 5 6 7 8 9 10

• 20
• 15
• 10
• 5

5 x 10

• 3

1 2 3 4 5 6 7 8 9 10 0.02 0.03 0.04 0.05 0.06 0.07

Responses to a contractionary productivity shock under optimal policy

OPTIMAL POLICY AND ASSET PURCHASES

26

1 2 3 4 5 6 7 8 9 10 0.2 0.25 0.3 0.35 0.4 1 2 3 4 5 6 7 8 9 10

• 3
• 2.5
• 2
• 1.5
• 1

x 10

• 3

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 x 10

• 3

φ=0.7 φ=0.1 1 2 3 4 5 6 7 8 9 10

• 6
• 5
• 4
• 3
• 2

x 10

• 4

1 2 3 4 5 6 7 8 9 10

• 4
• 3
• 2
• 1

1 2 x 10

• 4

1 2 3 4 5 6 7 8 9 10

• 8
• 7
• 6
• 5
• 4
• 3
• 2

x 10

• 3

Responses to a lower liquidation value under optimal policy w/o money rationing

OPTIMAL POLICY AND ASSET PURCHASES

27 Money rationing and loan purchases Policy rate below the lender’s marg. rate of intertemp. substitution, Rm

t < RL t

– Purchases of loans t > 0 tends to reduce the loan rate Non-optimizing policy (for z = 0:4) – Loan purchases with = 0:5 and = 1 – Optimal policy without money rationing is outperformed An extreme case (for z = 0:8) – Monetary policy sets t to slacken the borrowing constraint – Welfare loss (perm. consump.) relative to …rst best reduced by 75%

OPTIMAL POLICY AND ASSET PURCHASES

28 Steady state values for non-optimizing policies for z=0.4

Optimal policy w/o m. rationing Policy regime I with m. rationing Policy regime II with m. rationing First best Borrower’s consumption 0.3003 0.3004 0.3005 0.3018 Lender’s consumption 0.1744 0.1743 0.1742 0.1742 Housing of the borrower 0.6369 0.6150 0.5954 0.5 Working time 0.3233 0.3234 0.3234 0.3248 Loan rate 1.0044 1.0049 1.0052

–

In‡ation rate 1 1 1

–

Policy rate – 1.0040 1.0040

–

Share of purchased loans

–

0.5 1

–

• Rep. agent utility

–3.12145 –3.12126 –3.12112 –3.12078

OPTIMAL POLICY AND ASSET PURCHASES

29 Steady state values with and w/o money rationing for z=0.8

Optimal policy w/o money rationing Optimal policy with money rationing First best Consumption of the borrower 0.3009 0.3012 0.3018 Consumption of the lender 0.1739 0.1737 0.1742 Housing of the borrower 0.5334 0.5 0.5 Working time 0.3235 0.3236 0.3248 Loan rate 1.0091 1.0086

–

In‡ation rate 1 1

–

Policy rate – 1.0026

–

Fraction of purchased loans

–

0.6860

–

Representative agent utility –3.12086 –3.12083 –3.12078

OPTIMAL POLICY AND ASSET PURCHASES

30

2 4 6 8 10 12 14 16 18 20 0.05 0.1 0.15 0.2 0.25 0.3 0.35 1 2 3 4 5 6

• 0.4
• 0.35
• 0.3
• 0.25
• 0.2

1 2 3 4 5 6

• 0.4
• 0.35
• 0.3
• 0.25
• 0.2

Money rationing Non-rationing 2 4 6 8 10 12 14 16 18 20 0.05 0.1 0.15 0.2 2 4 6 8 10 12 14 16 18 20

• 1
• 0.5

0.5 1 1.5 2 x 10

• 3

2 4 6 8 10 12 14 16 18 20 0.01 0.02 0.03 0.04 0.05 0.06 0.07 2 4 6 8 10 12 14 16 18 20 0.01 0.02 0.03 0.04 0.05 0.06 0.07 2 4 6 8 10 12 14 16 18 20 0.5 1 1.5 2 2.5 2 4 6 8 10 12 14 16 18 20

• 0.8
• 0.6
• 0.4
• 0.2

Responses to a contractionary productivity shock under optimizing policies

OPTIMAL POLICY AND ASSET PURCHASES

31

2 4 6 8 10 12 14 16 18 20 0.1 0.2 0.3 0.4 2 4 6 8 10 12 14 16 18 20

• 3
• 2.5
• 2
• 1.5
• 1
• 0.5

x 10

• 3

2 4 6 8 10 12 14 16 18 20

• 1

1 2 3 4 5 x 10

• 3

Money rationing Non-rationing 2 4 6 8 10 12 14 16 18 20

• 6
• 4
• 2

2 x 10

• 4

2 4 6 8 10 12 14 16 18 20

• 2
• 1

1 2 3 4 5 x 10

• 5

2 4 6 8 10 12 14 16 18 20

• 8
• 6
• 4
• 2

x 10

• 3

2 4 6 8 10 12 14 16 18 20

• 0.01
• 0.005

0.005 0.01 0.015 0.02 2 4 6 8 10 12 14 16 18 20 0.5 1 1.5 2 2.5 3 2 4 6 8 10 12 14 16 18 20

• 0.02

0.02 0.04 0.06 0.08 0.1

Responses to a lower liquidation value under optimizing policies

32 I INTRODUCTION II THE MODEL III CONSTRAINED BORROWING AND MONETARY POLICY IV OPTIMAL POLICY AND ASSET PURCHASES V CONCLUSION

CONCLUSION

33 Optimal monetary policy under constrained borrowing – Conventional policy: central bank trade-o¤ hardly a¤ected by the credit friction When money supply is rationed – Central bank loan purchases can enhance welfare