Bernanke & Gertler (1989) - Agency Costs, Net Worth ...mkredler/ReadGr/KirkbyOnBernankeGertler89.pdf · Bernanke & Gertler (1989) - Agency Costs, Net Worth, & Business Fluctuations

Bernanke & Gertler (1989) - Agency Costs, Net Worth, & Business Fluctuations

Bernanke & Gertler (1989) - Agency Costs, NetWorth, & Business Fluctuations

Robert Kirkby

UC3M

November 2010


The Idea

Motivation

I Condition of firm & household often suggested as adeterminant of macroeconomic activity, eg.

I Miskin (1978) & Bernanke (1983) argue that the weakness ofborrowers’ balance sheets contributed to the severity of GreatDepression

I Eckstein & Sinai (1986) put firm balance sheets at the centerof their analysis of cyclical dynamics.

I Numerous studies have connected balance sheet conditionswith household & firm spending decisions.


The Idea

Agency Costs

I Introduce imperfect information into an RBC framework.

I Assume an information assymetry between entrepreneurs whoorganise and manage physical investment and the savers fromwhom they borrow.

I Specifically, assume a costly state verification problem(Townsend, 1979, 1988).

I This makes the Modigliani-Miller theorem inapplicable,opening up possibility of interaction between real and financial(ie. balance sheet) factors


The Model

The Model

I Use an RBC model, extended to a two-period OLG framework.

I Each individual lives two periods, can earn labour income onlyin the first, and so must save to finance the consumption inthe second.

I Saving can be done either in inventories or capital.

I Two goods produced, output good and capital.

I Capital good production is the one suffering from informationasymmetries.


The Model

The Agents

I Countable infinity of agents in each generation.

I Fraction η of agents in each generation are entrepreneurs.Rest are lenders.

I ω ∼ U[0, 1]; indexes productivity of the entrepreneurs(low ω =⇒ low cost)


The Model

The Goods

I Two goods: Capital good & Output good

I Output good can be consumed, invested as capital, or storedas inventory.

I One unit of output stored in period t yields r units in periodt+1 (r is gross rate of return).

I Capital fully depreciates each period (this is for expositionalreasons only).


The Model

Output production

I Production function for per-capita output is (assume thatlabour supply is fixed):

yt = θt f (kt) ,f (0) > 0, θt ∼ iid ,E (θ)) = θkt ≡ capital per head

θt ≡ agg. productivity shock


The Model

Capital production

I Each entrepreneur has a project they can invest in. It requiresan input of x(ω) (x is inc in ω).

I Any project undertaken in t, yields an amount of capital int+1 given by κi

I κi is an iid discrete random variable taking values i = 1, ..., n,κj > κk ,∀j > k

I The probability of outcome κj is πj , and the expectedoutcome is κ.

I Note that ω does not affect outcome, only required inputs.This is a simple way of motivating an upward-sloping supplycurve.


The Model

Asymmetric Information

I Project outcome is costlessly observable to the entrepreneurwho operates it. Any other agent must pay an audit cost, γunits of capital, which makes project outcome visible to allagents.

I We assume that there is no other way to determine theoutcome (eg. by looking at agents consumption). We assumerandom auditing is feasible (lenders can precommit to auditwith some probability).

I Chronologically; Project outcomes are realized,announcements are made (of realized κi ), and auditing takes

place before the current period value of θt .


The Model

Capital production cont.

I Investment project outcomes are mutually independent so ataggregate level there is no uncertainty about the level ofcapital produced. So,

kt+1 = (κ− htγ)itht ≡ fraction of projects initiated in t that are audited

it ≡ number of investment projects undertaken in t per-capita

I We also assumeθf ′(0)κ > rx(0) + γθf ′(κη) < rx(1)

Which guarantees that some but not all entrepreneurs willalways invest.


The Model

Labour Supply & Prefs

I Labour Supply= 1 = ηLe + (1− η)LL, Le ≡ labour endowment of lenders & entrepreneurs

I Lenders Prefs: U(zyt ) + βEt(zo

t+1)Follow Sappington (1983) in assuming risk-neutrality ofconsumption when old. This allows to concentrate on role of agentswealth in mitigating agency costs, rather than on issues ofrisk-sharing.

I Entrep. Prefs: Et(zot+1)

The assumptions that entrepreneurs & lenders have different prefs,& in particular, that entreprenteurs do not consume when young areinessential.


The Model

Wages & Savings

I Wage wt ; so entrepreneurs have per-capita incomes of wtLe

(lenders have wtL).

I Entrepreneurs do not consume when young, so avg.entrepreneurial savigns, Se

t , isSe

t = wtLe

I Solving lenders problem for optimal cons. when young as fn ofr , z∗y (r), avg. saving by lenders is

St = wtL− z∗y (r)

I Main importance of these to equations is to esablish a linkbetween wages (marg. productivities) & savings.


Equilibrium

Perfect Information Case, gamma = 0

I For ω ≤ ω, entrepreneurs make investment.

I q, the relative price of capital, and k are constant over time.Investment is fixed.

I So production of the output good fluctuates in proportion tothe (serially uncorrelated) productivity shock.

I Consumption is positively serially correlated with output.

I We will consider this as the benchmark case.


Equilibrium with Asymmetric Information

Optimal Financial Contract

I Look at optimal contract for entrepreneur who needs toborrow (x(ω) > Se).

I If entrepreneur announces κ2 there will be no auditing (n = 2)

I If Se is sufficiently large that, qκ1 ≥ r(x(ω)− Se), then agentis fully collateralized and there is no moral hazard problem.

I If Se is not this large, then we are in the incompletecollateralized case, & there will be positive agency costs. Cansolve for optimal auditing probability p.

I Note that when there is incomplete collateralization,∂cic∂Se = αr > r , that is, return to inside funds is higher thanreturn to outside funds (as lower agency cost).



Optimal Financial Contract

Agents’ problem is

maxπ1(pca + (1− p)c1) + π2c2

s.t

π1[qκ1 − p(ca + qγ)− (1− p)c1] + π2[qκ2 − c2]

≥ r(x − Se) Outside Option (r)

c2 ≥ (1− p)(q(κ2 − κ1) + c1) Incentive Compatibility

c1, ca ≥ 0 Limited Liability

0 ≤ p ≤ 1



Entrepreneurial Investment Decision

I Now consider whether investor will want to use his savings,and the effects of audit costs on his choice.

I Defining ω & ω by:qκ− rx(ω)− qπ1γ = 0qκ− rx(ω) = 0

I We distinguish 3 types of entrepreneur;I Good, ω ≤ ω; positive net exp. return on projects is always

positive (even if audit with prob. 1)I Fair, ω ≤ ω ≤ ω; exp. returns will be positive or negative

depending on auditing levelI Poor, ω ≤ ω; returns are negative even with zero auditing



I Again, for any ω, define full collateralization level ofentrepreneurial savings, S∗(ω) to be

S∗(ω) = x(ω)− (q/r)κ1

I And, for fair entrepreneurs, defining S ′(ω) as the saving levelthat makes investment have the same rate of return asstorage.

I We get that, all good entrepreneurs invest, all poor do not,and a fraction of the fair do.

I Only the good will be audited (as they use a lottery on the fairso the fraction that does invest all ends up fully-collateralized)



Within-Period Equilibrium

I Let p(ω) be probability of audit for good type, and g(ω) thefraction of fair type who invest.

I Total capital formation (per capita), taking kt given, is then

kt+1 = [κω −∫ ω

0 π1γp(ω)dω]η + [κ∫ ωω g(ω)dω]η

I This gives kt + 1 as a function of qt+1. The demand functionis the same as for the perfect information case.


Macro-Implications of Model

Statics

Compartive Statics

I k is lower with γ > 0 than benchmark full information case,gamma = 0.

I An increase in current incomve (either higher inherited kt orhigher θt) will increase entrepreneurial savings, Se , loweringagency costs, and thereby increasing kt+1.

I Debt-deflation: raise L & lower Le . The motivation for thisexercise is to model unindexed debt contracts & unexpecteddeflation redistributing wealth from the debtor class to thecreditor class. Decreasign Le , lowers Se , increasing agencycosts and thus leads to lower investment kt+1.



Dynamics

Aggregate Dynamics

I Consider a productivity shock. In the informationallyconstraint region, a (temporary) rise in θ stimulatesinvestment by increasing net worth. The expansion persistsbecause the rise in the future capital stock makes investmentin the subsequent period higher than it would otherwise be.

I The intuition; In good times, when profits are high & balancesheets are healthy, it is easier for firms to obtain outside funds.This stimulates investment & propagates the good times.

I Vice-versa for bad shock/times.



Dynamics

I This is the finacial accelerator effect; income has a sort ofaccelerator effect on investment. Note that countercyclicalagency costs are crucial to the story.

I A redistributional shock (ie. the debt-deflation case describedearlier) will instigate a similar sort of dynamics. Thus, balancesheet considerations may initiate, as well as propagate,cyclical fluctations.



Dynamics

Conclusions

I The existence of countercyclical agency costs that cause anydeviations from first-best outcomes associated with thenecessity of external finance will generate an acceleratoreffect, in which financial (balance sheet) effects increase thesize of business fluctuations.

I They also mean that financial shocks can have real effects.

Documents

Bernanke & Gertler (1989) - Agency Costs, Net Worth ...mkredler/ReadGr/KirkbyOnBernankeGertler89.pdf · Bernanke & Gertler (1989) - Agency Costs, Net Worth, & Business Fluctuations