Monetary Paper 2

8/3/2019 Monetary Paper 2

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Introduction

Model

Credit Policy

Crisis Simulations and Policy Experiments

Conclusion

Motivations

Objectives

2008/2009 Crisis

Motivations

Old Motivation (for BGG 1999)

Mark Gertler and Nobuhiro Kiyotaki Financial Intermediation and Credit Policy in RBC
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Introduction

Model

Credit Policy


Conclusion

Motivations

Objectives

2008/2009 Crisis

Motivations

Old Motivation (for BGG 1999)Great Depression.

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Introduction

Model

Credit Policy


Conclusion

Motivations

Objectives

2008/2009 Crisis

Motivations

Old Motivation (for BGG 1999)Great Depression.Emerging market crises over the past quarter century.

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Introduction

Model

Credit Policy


Conclusion

Motivations

Objectives

2008/2009 Crisis

Motivations


New Motivation

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Introduction

Model

Credit Policy


Conclusion

Motivations

Objectives

2008/2009 Crisis

Motivations


New Motivation

Global economy during Bernankes tenure as Fed Chair

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Introduction

Model

Credit Policy


Conclusion

Motivations

Objectives

2008/2009 Crisis

Objectives

Their goal are two folds:

to illustrate how disruptions in financial intermediation can

induce a crisis that affects real activity;

to illustrate how various credit market interventions by the

central bank and/or the Treasury might work to mitigate the

crisis.

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Introduction

Model

Credit Policy


Conclusion

Motivations

Objectives

2008/2009 Crisis

Aspects of the Crisis they Tried to Capture

Disruption of Financial Intermediation

Much of the recent macro literature has emphasized creditfrictions on nonfinancial borrowers and has treatedintermediaries largely as a veil.

Unconventional Monetary Policy

to combat the crisis, both the monetary and fiscal

authorities in many countries including the US. haveemployed various unconventional policy measures thatinvolve some form of direct lending in credit markets.

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Introduction

Model

Credit Policy


Conclusion

Motivations

Objectives

2008/2009 Crisis

Approach

their plan is to look both forward and backward

Looking Forward: to offer a canonical framework to think

about credit market frictions and aggregate economicactivity in the context of the year 2008/2009 crisis.

Looking Backward: previous literatures were sourced todevelop the particular framework they offered and howsame could impact on the crisis

CAVEAT in using Canonical Framework1 Not a comprehensive or complete description2 Only a first pass at organizing thinking3 Goal is to lay out issues for future research

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Introduction

Model

Credit Policy


Conclusion

Motivations

Objectives

2008/2009 Crisis

Unconventional vs. Conventional Monetary Policy

Conventional: The central bank adjusts the short term rate

to affect the market structure of interest rates.Unconventional: The central bank lends directly in private

credit markets.

Section 13.3 of the Federal Reserve Act: "In unusual and

exigent circumstances.. the Federal Reserve may lend

directly to private borrowers to the extent it judges the

loans to be adequately secured."

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Introduction

Model

Credit Policy


Conclusion

Motivations

Objectives

2008/2009 Crisis

What they did

Develop a quantitative DSGE model that allows for

financial intermediaries that face endogenous balancesheet constraints

Use the model to simulate a crisis that has some of the

features of the 2008/2009 downturn.

Assess how unconventional monetary policy (direct centralbank intermediation.) could moderate the downturn.


I d iFramework
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Introduction

Model

Credit Policy


Conclusion

Framework

Firm

Households

Financial intermediaries

Non-Financial Firms

Equilibrium

Retail Financial market


I t d tiFramework
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Introduction

Model

Credit Policy


Conclusion

Firm

Households


Non-Financial Firms

Equilibrium

wholesale credit/financial market


IntroductionFramework
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Introduction

Model

Credit Policy


Conclusion

Firm

Households


Non-Financial Firms

Equilibrium

Physical Environment: Firm

Firm dispersed across islands, with perfectly mobile labor:

Yt = AtK

t L1t

I.I.D. prob. i of arrival of investment opportunities across

islands.The law of motion for capital becomes

Kt+1 = [t(It + i(1 )Kt)] + [(1

i)t(1 )Kt]

= [t(It + i(1 )Kt)]

Resource Constraint Yt = Ct + [1 + f(It

It1)]It + Gt


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Introduction

Model

Credit Policy


Conclusion

Firm

Households


Non-Financial Firms

Equilibrium

Physical Environment: Households

Within each household, 1 f "workers" and f "bankers".

Workers supply labor and return their wages to the

household.

Each banker manages a financial intermediary and also

transfers earnings back to household

Perfect consumption insurance within the family.


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Introduction

Model

Credit Policy


Conclusion

Firm

Households


Non-Financial Firms

Equilibrium

Physical Environment: Households contd

To limit bankers ability to save to overcome financial

constraints:

With i.i.d prob. 1 , a banker exits next period. (averagesurvival time= 11 )

Upon exiting, a banker transfers retained earnings to the

household and becomes a worker.

Each period, (1 )f workers randomly become bankers,keeping the number in each occupation constant

Each new banker receives a "start up" transfer from the

family.


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Introduction

Model

Credit Policy


Conclusion

Firm

Households


Non-Financial Firms

Equilibrium


Et

i=0

i[In(Ct+i Ct+i1)

1 + L1+t+i ]

s.t

Ct = WtLt + t + Tt + RtDt Dt+1

Dt = short term bonds (intermediary deposits and

government debt)

t= payouts to the household from firm ownership net thetransfer it gives toits new bankers.



Fi
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Introduction

Model

Credit Policy


Conclusion

Firm

Households


Non-Financial Firms

Equilibrium


foc

Et(uct)Wt = L

t (1)

Ett,t+1Rt+1 = 1 (2)

t,t+1 = uct+1uct



Firm
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Model

Credit Policy


Conclusion

Firm

Households


Non-Financial Firms

Equilibrium

Physical Environment:Financial Intermediaries(Banks)

with perfect interbank market

Intermediary Balance Sheet

Qtst = nt + bt + dt

Evolution of Net Worthnt+1 = Rkt+1Qtst Rt+1dt

while cost of borrowing becomes

nht = [Zt + (1 )Qht ]tst1 Rbtbt1 Rtdt1



Firm
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Model

Credit Policy


Conclusion

Firm

Households


Non-Financial Firms

Equilibrium

Banks contd

the objective of the bank at the end of period t is the expected

present value of future dividends which is

Vt

= maxEt

i=1(1

)it,t+i

(nt+i

)

Banks constraint:1 Divertable assets consists of total gross assets

Qht sht (fraction of interbank borrowing)

2 if =1 (i.e banks cannot divert assets financed by borrowing

from other banks) therefore, interbank market operatesfrictionlessly,and banks are unconstrained in borrowingfrom one another but constrained from depositors.

3 but the contrast occurred if =0



Firm
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Model

Credit Policy


Conclusion

Firm

Households


Non-Financial Firms

Equilibrium

Financial Intermediaries (Banks) contd

Bellman equation that satifies the value of the bank is

Vt1(st1,bt1,dt1) = Et1t1,t

h=i,n

h{(1 )nt+

maxdt

[maxsht ,b

ht

Vt(sht ,b

ht , d

ht )]}

the incentive constraint which must hold for Banks not to

divert becomesVt(s

ht ,b

ht ,dt) (Q

ht s

ht b

ht )

the decision problem are solved by guessing the linear

value function Vt(sht , b

ht ,dt) = sts

ht btb

ht tdt



Firm
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Model

Credit Policy


Conclusion

Firm

Households


Non-Financial Firms

Equilibrium

Financial Intermediaries (Banks) contdthe Foc for dt, s

ht ,

ht respectively of the value function becomes;

(bt t)(1 + t) = t( stQht bt)(1 +

ht =

ht(1 ))

[ ( stQht t)]Qht sht [ (bt t)]bht tnht (incentive

constraint)

if bt > t provided incentive constraint bind for some state

( > 0) then > 0 i.e inter-bank market operates more

efficiently than the retail deposit market.ht is the the Lagrangian multiplier for the incentive

constraint while

=

hhht is the average of this multiplier across states.


Introduction

M d l

FrameworkFirm
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Model

Credit Policy


Conclusion

Firm

Households


Non-Financial Firms

Equilibrium

Financial Intermediaries contd

With Frictionless Capital Markets ( = 1):

perfect arbitrage in the interbank market equalizes theshadow values of assets in each market, such that st

Qbt

= stQ

lt

andst

Qbt= bt

while = stQt t > 0 (excess value of assets)

banks are constrained in the retail deposit market such that

Qtst bt = tntThe higher the t the greater the franchise value of thebank and the less likely it is to divert funds.

and the demand for total assests becomes QtSt = tNt.


Introduction

M d l

FrameworkFirm
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Model

Credit Policy


Conclusion

Households


Non-Financial Firms

Equilibrium

Financial Intermediaries (Banks) contdCapital Markets with frictions ( = 0):

interbank loans and deposits become perfect substitutes assources of finance, therefore bt = t

if the constraint on inter-bank borrowing binds, then friction

limit Arbitrage opportunity by keeping Qi < Qn and

there is likelihood that banks on non-investing islands will

earn zero excess returns on their assets while the banks

on investing island earn a higher return.

higher return results in financial constraints to the banks inthe investing islands and the bank can divert funds

crisis is associated with a rise in excess return for banks

on investing islands and a rise in dispersion of returns

between island types


Introduction

Model

FrameworkFirm
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Model

Credit Policy


Conclusion

Households


Non-Financial Firms

Equilibrium

Evolution of Banks Net worth

The total net worth for type hbanks, Nht is

Nht = Nhot + N

hyt

Not is (old) existing entrepreneurs andNyt is (young) entering entrepreneurs

old entrepreneurs is

Not = h{[Zt + (1 )Q

ht ]tSt1 RtDt1}

whle existing entrepreneurs is

Nyt = [Zt + (1 )Qht ]tSt1

the banks balance sheet (Total Deposits) becomes

Dt =h=i,n(Q

h

tS

h

t N

h

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Introduction

Model

FrameworkFirm
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Model

Credit Policy


Conclusion

Households


Non-Financial Firms

Equilibrium

Goods Producers:

operate in a perfect market with CRS technology and

choose capital and labor inputs and the Euler becomes

ZtWt = (1 )YtLt

and gross profits per unit of capital

becomes

Zt =YtWtLt

Kt= At(

Lt

Kt)(1)

Issue state-contingent claims (equity) to obtain funds from

a financial intermediary and use the funds to buy new

capital goods from capital producers.

thus, in a perfect competition, the price of new capita

goods =Qit and goods producers earn zero profits.


Introduction

Model

FrameworkFirm
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Model

Credit Policy


Conclusion

Households


Non-Financial Firms

Equilibrium

Capital good producers

:

operate in a national market: They make new capital using

input of final output and subject to adjustment costs

They sell new capital to firms on investing islands andchoose I to solve

MaxEt

=t

t,(QiI [1 + f(

It

It 1)]I)

the price of capital goods (Qi) = the marginal cost ofinvestment goods production.

in equilibrium the market for goods, labor, securities and

inter bank loans cleared.


Introduction

Model

FrameworkFirm
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Model

Credit Policy


Conclusion

Households


Non-Financial Firms

Equilibrium

Equilibrium

Total securities issued on investing and non-investingislands correspond to aggregate capital such thatSit = It + (1 )

iKt (Investing island) andSnt = (1 )

nKt (Non-investing island)

labor demand equals labor supply such that(1 )Yt

Lt.Etuct = L

t

the market for riskless debt will also cleared such that

supply of government debt equals supply of private debt

and Dht = Dt + Dgtthe model reduces to a real business cycle while

balance sheet constraints on banks ability to obtain funds

may limit real investment spending, affecting aggregate

real activity in a friction credit market.


Introduction

ModelLending Facilities

Li idi F ili i
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Model

Credit Policy


Conclusion

Liquidity Facilities

Equity

Government

direct lending

Central bank intermediation supplements private

intermediation such that QtSt = QtSpt + QtSgtThe central bank issues government debt that pays Rt+1

and then lends to nonfinancial firms at Rkt+1Efficiency cost of per unit of govt credit provided.

the central bank is not "balance-sheet" constrained.

central bank chooses the fraction t of the the total credit

market to intermediate such that QtSgt = tQtSt

where t is the instrument of central bank credit policy.if n > 0 i.e if excess return ( balance sheet constrained)

exist, lending facilities affect asset demands.

but if n = 0 central bank credit provision crowds outprivate intermediation


Introduction


Li idit F iliti
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Credit Policy


Conclusion


Equity

Government

Discount window lending

they assume =0 therefore Rbt+1 = Rt+1The flow of funds constraint with discount window lending

becomes Qht sht = n

ht + b

ht + m

ht + dt

the incentive constraints becomesVt(nht , b

ht ,m

ht ,dt) (Q

ht s

ht tm

ht )

the market demand for asset by investing banks is given by

QitSit =

itN

it + gMt

So as long as > 0 discount window lending can expand

the total level of assets.if nt <

it bank on non- investing island will not borrow

from the discount window.

therefore, discount window will be too expensive for banks

who do not have investment to fund.


Introduction


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Credit Policy


Conclusion


Equity

Government

Equity Injections

government injects equity into banks who stay active

banks balance sheet becomes Qtst = nt + bt + dt + ngtgovt might pay premium QgtQt > 0 because the market

price is below the normal value due to financial crisis.aggregate asset demand and evolution of networth

becomes QtSt = tNt + Ngt and Nt = ( + )[Zt + (1 )Qt]tSpt1 RtDt1 + (QgtQt)[Sget (1 )tSget1]ngt = Qtsget where nt implies the market value of govt

equitybecause Ngt = QtSget where Ngt implies the totalgovernment equity in the banking system where Sgetimplies the total holdings of government equity.

equity injection expands private bank net worth


Introduction


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Credit Policy


Conclusion


Equity

Government

Government Budget Constraints

Government consumption consist of government

expenditures Gand intermediation expenditures such that.

Gt = G+ eSget +

h=i,nShgt

government expendituresGare financed by lump sumtaxes Tt and net earnings from credit market interventions

as

Tt + Ztt(Sgt1 + Sget1) + RmtMt1 Mt + Dgt RtDgt1during the crisis the government will earn extra returns on

its portfolio but private intermediaries are constrained from

exploiting this.

However, government may takes losses on its portfolio but

lump sum taxes adjust to finance the losses


Introduction

Model
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Credit Policy


Conclusion

Impulse Response

Calibration

To compensate partly for the absence of labor market

frictions, they use Frisch labor elasticity of 10 while

business cycle literature lies btw 1 and 3.

there are eleven parameters seven are standard

preference and technology parameters which includes

,,,,,,

they added 4 additional parameters which includesi, , and


Introduction

Model
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Credit Policy


Conclusion

Impulse Response

Parameters


Introduction

Model

C dit P li I l R
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Credit Policy


Conclusion

Impulse Response

No Policy response


Introduction

Model

Credit Policy Impulse Response
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Credit Policy


Conclusion

Impulse Response

No Policy response


Introduction

Model

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Credit Policy


Conclusion

Impulse Response

Credit Policy Response

The financial crisis is largely due to the increase in the

spread between the expected return on capital on

investing islands and the riskless interest rate.the existence of the spread afford the Fed to intervene with

credit policy.

Fed adjust the fraction of private credits it intemediates to

the difference between spreads on investment islands andits steady state value as

= vg[(EtRhkt+1 Rt+1) (ER

hk R)]


Introduction

Model

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Credit Policy


Conclusion

Impulse Response

Credit Policy response


Introduction

Model

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Credit Policy


Conclusion

Impulse Response

Credit Policy response


Introduction

Model

Credit Policy
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Credit Policy


Conclusion

Conclusion

Overall effect,

net welfare benefits from the credit policy intervention canbe evaluated,

the net benefits to the intervention are large and

approximately equal to the gross benefits.

the intervention of the Central Banks cause net benefit to

increase in the severity of the crisis.

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Monetary Paper 2

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