holmstrom slides

8/12/2019 Holmstrom Slides

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INSIDE AND OUTSIDE LIQUIDITY

by Bengt Holmstrom(based on joint work with Jean Tirole)

February 2008


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INTRODUCTION

Background:

Micro: demand for liquidity, risk management, asset pricing Macro: supply of liquidity, financial crises, liquidity

management

Basic questions:

Do claims on corporate assets provide sufficient liquidity foran efficient functioning of the productive sector?

What role, if any, should the government play in supplyingand managing liquidity?

How does access to international financial markets affectaggregate liquidity constraints?

Underlying premise:

All financial claims must be backed by real (non-human)assets

No other exogenous restrictions on financial claims


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WHY DO FIRMS DEMAND LIQUIDITY?

Demand for liquidity = Demand for long-term financialinstruments

No corporate demand for liquidity: in standard theory --- firms can finance all positive net

present value projects on an as-needed basis in standard liquidity approach (Diamond-Dybvig)

Key ingredient: the full value of a firm cannot be promised to outside

investors (z1> z0)

Three reasons why z1> z0: Adverse selection (eg. liquidity traders lose to informed

traders) Moral hazard (eg. entrepreneur has to be given incentives not

to steal or to put out proper effort)

Search costs

Firms want ex ante insurance against shocks to liquidity

0 z0 z1

pledgable non-pledgable


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OUTLINE OF TALK

Demand for liquidity

Credit rationing Liquidity shocks

Private supply of liquidity

Liquidity shortages Endogenous supply of liquidity Liquidity premia and asset pricing

Government supply of liquidity

Government bonds State-contingent bonds

International liquidity International vs domestic collateral


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CREDIT RATIONING

(z1 z0)I external

I z1I

z0I internal

Assume: z0 < 1 < z1

Program: U = max (z1 z0)II

s.t. zoI I A

Solution: I =-1

A

0z

U =)z1(

)z(zA

0

01

> A


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DEMAND FOR LIQUIDITY

Add liquidity shocks: z = zL or z

H (for simplicity only two outcomes)

contract shockz continuezi(z) (z1 z0)i(z)

liquidate

0

Assume: zL < z0 < 1 < zH < z1

Program: max (z1z0) (pL+ pHx) Ix,I

s.t. pL(z0zL)I + pHx(z0zH)I I A

> 0 < 0

Negative NPV in H-state all insurance has that feature


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SECOND-BEST SOLUTION

Investment: I = )z(p)z(p1

A

0H0L HL zxz

Reinvestment: x = 1 if and only if pL(zH zL) 1

Note: Ix=0 > Ix=1

zL zH0 z0 1 z1

Continuous distribution F(z):

z*

0 z0 1 z1

Discontinue

*

0

1=)dF(z

zz

U = 0

1

z*

*-z

z

z

A

Credit rationing at date 0 and date 1.


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THE SUPPLY PROBLEM

Equilibrium model:

Single non-storable good (corn) Individual preferences: c0+ c1 + c2; suffiently largeendowments

Many firms with identical (two-state), CRS technologies

Key constraint: consumers cannot borrow against future endowment(financial commitments have to be backed by real assets)

How can liquidity shocks be financed? Issue new securities at date 1 (initial shareholders are junior) Buy securities in other firms at date 0 and sell at date 1

Pure aggregate shock: only self-financing possible.Can raise up to z0I in new funds at date 1.

self-financing works if z = zL < z0doesnt work if z = zH > z0

0 zL z0 zH z1

Self-financing External financing


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COORDINATING LIQUIDITY DEMAND

Independent shocks:

Demand: pH(zHz0) I

Supply: pL(z0 zL) I

Supply > Demand ? Yes, because:

pL(z0zL) I + pH(z0zH) I I A > 0

However: Market instruments may not suffice. Compare date-1 valueof share in market index (after refinancing) with liquidity demand byfirm with high liquidity shock:

S = z0pHzHpLzL zHz0

For small enough z0this condition is violated.

Problem: Firms with low liquidity shock are wasting scarce liquidity.

Solution: Intermediation


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INTERMEDIATION

Intermediary can eliminate waste by coordinating liquidity demand by

firms. Market index is worth

S = z0pHzHpLzL> I A > 0

so there is enough aggregate liquidity.

Intermediary

Issues shares to consumers at date 0

Invests proceeds in market index (buys all public claims onthe corporate sector)

Issues credit lines to firms. Allows each firm to draw up to zHI at date 1.

Result

Assuming firms have no other use for funds, they will drawzHor zLaccording to need.

By investing in market index at date 0, credit lines fullybacked by claims on productive assets. Intermediation cross-subsidizes firms with high liquidityshocks (who end up with negative NPV reinvestments). Towork, credit lines must have commitment fees.

Intermediation provides insurance a la Diamond-Dybvig (but withmarkets playing a positive role).

Liquidity supply the two questions: Is there enough aggregate pledgable income in each state? Is the financial system making optimal use of it?


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ENDOGENOUS LIQUIDITY SUPPLY

Pure aggregate shock: all firms experience either high liquidity

demand zHor low liquidity demand zL.

Add a storage technology(a short-term technology). Cost ofproduction (could come from govt supply):

i0 = C(LS)

Date 0 cost of producing LSunits of date 1 good is i0. Storage is riskfree.

Let q 1 be the date-0 price of one unit of pledgable date-1 corn (=date-1 liquidity).

Firms budget constraint becomes:

pL(z0zL) I + pH(z0zH)xI (I A) + (q 1)(zHr)xI

The firms demand function:

0, for q > qmaxD(q) = x(q)I(q)(zHz0) =

I(q)(zHz0), for q < qmax

(x in (0,1) for q = qmax)

Supply function LS(q)

q = C(LS(q))


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Equilibrium characterized by:

liquidity premium qE1 > 0, when there is a shortage ofliquidity

only firms buy claims on storage technology efficiency

Example of endogenous supply: mortage backed securities = increasing z0through monitoring

(net increase depends on what funds spent on)

Equilibrium with liquidity premium

LS

LD

qmax

qE> 1

LE

q = 1


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EMPIRICAL EVIDENCE OF SCARCE SUPPLY Krishnamurthy&Jorgense-Vissing 2007


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GOVERNMENT BONDS

Assume: Government can commit funds on behalf of consumers by

virtue of taxation right. Can make inter-generationaltransfers.

Bond: Date-0 price q 1

Date-1 price = 1

If q = 1, then firms can implement second-best:Reduces date-0 investment

Reduces date-1 liquidationAggregate investment goes upValue of firms go up

Liquidity premium (q > 1) to cover deadweight loss of taxation:Only firms buy government bonds

Lower aggregate investmentBias towards ex ante investment (and more generallytowards investments that fetch liquidity premium; shorter

investment horizons to build up liquidity stock)

Free-riding: Resolution: state-contingent bonds.


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STATE-CONTINGENT BONDS

When z = zL, firms will cash government bonds even though theydont need liquidity. Wasteful taxation.

More efficient to use state-contingent bond:

z = zL bond pays 0

z = zH bond pays 1

Lower liquidity premium, since dead-weight loss smaller

More efficient than having private sector create real assets

Key feature: Transfers income from consumers to producers

Interpretations:

Monetary policy; lower interest rate increases value of bond.Requires dynamic model.

Discount window (??)

YK2 put options (insurance markets)

Many other ways government creates liquidity (eg unemploymentinsurance)

A metaphor for any active government policy that transfers wealth

from consumers to producers.

What about taxing consumers in recession? Depends on nature ofshocks. Need to look at consumer and producer demand for liquidity.


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FACTORS AFFECTING AGGREGATE LIQUDITY--- MONITORING BY INTERMEDIARY

Without monitoring:

external internal

0 r R

With monitoring:

external monitor internal

0 z0 zm z1

Monitor can restrict misbehavior or extract more out of entrepreneurthan general market (Holmstrom-Tirole QJE 97; Diamond-Rajan JPE)

Monitoring allows financing of marginal firms. Well capitalized firmsand firms with marketable assets will not need monitor.

Monitoring incentives require monitor to invest capital (could bereputation). When capital scarcity increases, marginal firms will beexcluded (flight to quality).


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FACTORS AFFECTING AGGREGATE LIQUIDITY--- OPPORTUNISM

Ex post opportunism:

Entrepreneur can divert unused credit line for own private benefit(eg consumption)

Extreme case: divert all of it for own consumption

Non-discretionary credit lineLimited dilution of initial claims

Dilution contingent on aggregate shock only

Demand for active monitoring of credit use


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ASSET LIQUIDATION AND MARKET SOFTNESS

t = 0 t=1 t=2 (z1z0)(IL)

Liquidate LProceeds v(L)L

Problem: Uncoordinated liquidation may lead to market collapse

Example:v, if L L*

v(L) =0, if L > L*

Assume L* i (IiAi) + k qkLk

qk1 = E0(k| H)sHpH

sH -- shadow price of liquidity in state H

q

q

E

E0

0

k

l

k

l

H

H

=1

1

( | )

( | )

Co-movements Skewed risk tolerance Most efficient asset pays only in state H


20/26

1 International insurance with identical firms

Three periods,t = 0, 1, 2.

Goods and preferences.

Tradable goods (dollar goods) consumed by foreigners as well as do-mestics. Variables referring to dollars are starred

Nontradable goods (peso goods) consumed only by domestics. Pesosare used as numeraire.

Preferences.

Foreigners utility from the consumption stream {ct}t=0,1,2

2X

t=0

ct ,

Domesticsutility from the consumption stream{(ct , ct)}t=0,1,2

2X

t=0

[ct +ct] .

State of nature (revealed at date 1). Price of a peso delivered at date1s()f(). Price of dollar delivered at date 1 s()f()

Date-0 real exchange rate, e, (peso price of a dollar),. Date-1 exchangerate e1 iss

()/s(). In equilibrium, e, e1 1.

1


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Firms and technologies.

Unit mass offirms (=entrepreneurs). Peso endowmentA, dollar endow-mentA.

External supply of date-1 peso goods L and dollar goodsL (eg suppliedby government)

Date 0: Firms invest I,I.Date 1: Conditional on the realized state of nature , firms make re-

investmentsi()and i(), costing z(),z().Date 2: Pledgeable payoffs z0() and z

0() as well as the total payoff

z1(), are realized. The non-pledgable private benefitz1() z0() z

0()

is always strictly positive.

Collateral.

International collateral z0

()Domestic collateral z0() +z

0().

Foreign investors can secure pledges at no cost using collateral on inter-national markets. When domestic dollar assets are scarce, there is a pesopremium on international collateral.

2


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Equilibrium.

The representative firm chooses its production plan (initial investmentsand continuation decisions) to solve the following program:

Max E(Z1() Z0() Z

0())

(I A) +e(I A) +E[l()s() +l()s()] 0. (1)

Z0() Z() +l() +t() 0, for every (2)

Z0

() Z() +l() t() 0, for every (3)

(i(), i()) D(I, I)and t() 0. (4)

Two equilibrium conditions, determine the price of dollar goods at dates0 and 1.

Peso liquidity in state (givess()):

l () L(), for every , withs() = 1 if constraint is slack. (5)

Date-0 zero dollar market clearing (gives e):

I +El() A +EL

(), . with e = 1 if constraint is slack. (6)

Note:e=s() 1 for every . (7)

e=s() s() 1. (8)

3


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1.1 Example 1: All output tradable

Entrepeneurs endowment A > 0, A = 0..Date 0 investment I . Date 1,reinvestment zi(z), i(z) IDate 2 output all in dollars z

0i(z) with private

benefit (z1 z

0)i(z).

Since all pledgable output in dollars, theres no liquidity shortage (firmcan buy insurance on international markets).

e=s(z) =s(z) = 1. (9)

Firm solvesI and{i(z)} by

max {Ez[(z1 z

0)i(z)]} (10)

s.t.

(i) I A Ez[(z0 z)i(z)],

(ii) 0 i(z) I, for allz .

Optimal continuation rule: i(z) = I if z z and i = 0 otherwise, whereoptimal cut-offz satisfies

z0


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1.2 Example 2: Tradable and non-tradable outputs

In Example 1, no role for government supplied liquidity, because internationalinvestors willing to supply liquidity at zero premium. When a countrys inter-national collateral is scarce, theres a role for government supplied domesticliquidity.

All investments still in pesos. In addition to pledgeable dollar outputz0

i(z)there is now pledgeable peso output z0i(z).Entrepreneur has endowmentsA andA Government suppliesL units of

one-period dollar bonds andL units of peso bonds at date 0.

Firm choosesI andi(z)to solve

max {Ez[(z1 z0 z

0)i(z)]} (12)

s.t.

(i) (I A) +e(I A) +Ez[l(z)s(z) +l(z)s(z)] 0,

(iia) (z0 z)i(z) +l(z) +t(z) 0, for allz

(iib) z0

i(z) +l(z) t(z) 0, for allz .

(iii) 0 i(z) I andt(z) 0 for allz .

Equilibrium prices are determined by

l(z) L, for everyz with equality whenever s(z)> 1.

and

I +Ez[l(z)] A +L, with equality whenevere >1.

5


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)(zzi

L

0*

zz 0zz )( 0zz

International

Liquidity

Domestic Liquidity

*LL +

Demand for liquidity

When dollars scarce relative to pesos e = s(z)> s(z) 1.The optimalsolution is characterized by five regions encountered in order asz increases:

(i) i(z) =I,zI L, t(z) = 0(ii) i(z) =I, L < zI < L+L,t(z)> 0

(iii)

(iv)(v)

i(z)< I, zi(z) =L+L, t =L.

i(z)< I, zi(z) =L, t

= 0i(z) = 0

When the liquidity shock z can be met with pesos, the firm will do so.

Dollars are scarce and will be used only in statesz where shock exceedsavailable peso liquidity.

Price of dollars (e > 1) will not vary with the state, because interna-tional insurance markets have no liquidity constraints.

The price of peso liquidity will vary, because of state-contingent liquid-ity constraints: s(z) = 1, in unconstrained states and s(z) = s(z) =

e >1 in constrained states.

International financial markets will alleviate, but not remove need fordomestic liquidity management.

6


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CONCLUSIONS

Simple framework for studying supply and demand of liquidity by

firms.

Supply of liquidity determined by two factors:o Aggregate liquidity = total value of productive goods and

services (in each state); base for contractingo Optimal coordination of liquidity = state-contingent use of

liquidity; waste of liquidity

Corporate governance and intermediation affect both pledgable

income (aggregate liquidity) and waste of liquidity

Capital poor countries: small base and suboptimal use of it

Government can act as intermediary between consumers andcorporate sector: insurance by transferring wealth

Many forms of government insurance: monetary policy,unemployment insurance, devaluations, etc.

International financial markets can provide insurance to the extentcountry has international collateral.

Government as well as international insurance in states withliquidity shortage.

Undersupply of international insurance if aggregate liquidity

imperfectly coordinated.

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