Financial Intermediation and Credit Policy in Business Cycle Analysis∗ pot

F in a n c ia l Inte r media tio n and C r e d it Po lic y
in
B usiness C y cle A n alysis
∗
Mark Gertler and Nobuhiro Kiyotaki
N.Y.U. and Princeton
October 2009
This version: Marc h 2010
Abstract
We develop a canonical framework to think about credit mark et
frictions and aggregate economic activity in the context of the current
crisis. We use the framework to address two issues in particular: first,
how disruptions in financial intermediation can induce a crisis that
affects real activity; and second, how various credit mark et interven-
tions by the central bank and the Treasury of the t ype we have seen
recently, migh t work to mitigate the crisis. We make use of earlier
literature to develop our framework and characterize how v ery recent
literature is incorporating insights from the crisis.
∗
Prepared for the Handbook of Monetary Economics. Thanks to Mic hael Woodford,
Larry Christiano, Simon Gilc hrist, Chris E rceg, and Ian Dew-Becker for helpful comments.
Thanks also to Albert Queralto Olive for excellent research assistance.
1
1 Introduction
To motivate interest in a paper on financial factors in business fluctuations
it use to be necessary to appeal either to the Great Depression or to the
experiences of man y em erging m ar ket economies. This is no longer necessary.
Over the past few y ear s the Un ited States and muc h of the industrialized
world have experienced the worst financial crisis of the post-war. The global
recession that has follo wed also appears to have been the most sev ere of this
era. Atthetimeofthiswritingthereisevidencethatthefinan cial sector has

stabilized and the real economy has stopped con tractin g and output grow th
has resumed. The path to full reco very, howev er, remains highly uncertain.
The timing of recent ev en ts, though, poses a challenge for writing a Hand-
book chapter on credit m arket f rictions and aggregate econ om ic activity. I t
is true that o ver the l ast s everal decades there has been a robust literature
in this area. Bernanke, Gertler and G ilc h rist (BGG, 1999) surveyed much
of the earlier work a decade ago in the Handbook of Macroeconomics. Since
the time of that sur vey, the literatur e has contin ue d to grow. W hile muc h
of this work is relevan t to the current situation, this literature obviously did
not anticipa te all the key empirical phenomena that have played out during
the current crisis. A new literature that builds on the earlier wo rk is rapidly
cropping up to address these issues. Most of these papers, though, are in
preliminary working paper form.
Our plan in this c hapter is to look both forward and backw ard. We loo k
forward in th e sen se tha t we offer a canonical framework to t hink about c red it
mar ket frictions and ag grega te econ om ic a ctivity in the context of the current
crisis. The framework is not m eant as com pr ehensive description of recent
ev ents but rather as a first pass at characterizing some of the k ey aspects and
at laying out issues f or future research. We look backward by making use of
earlier litera tu re to develop the particular fra m ework we o ffer. In d oing so,
we address how this litera ture ma y be relevan t to the new issues that h av e
arisen. We also, as best we can, chara cterize ho w v ery recen t literature is
incorporating insights from the crisis.
From our vantage, there are two broad aspects of the crisis that have not
been fully captured in w ork on financial factors in business cycles. First, by
all a cco unts, the cur rent crisis has featured a sign ifican t disruption of financial
2
intermediation.
1
Mu ch of the earlier macroeconomics literature w ith financial

frictions emphasized credit m arket c on straints o n non-financial borro wers and
treated intermediaries largely as a v eil (see, e.g. BG G ). Second, to com bat the
crisis, both the m on etary and fiscal a uthorities in man y coun tries including
the US. have emplo y ed various u nconventional policy m easures that in volv e
some form of direct lending in credit markets.
From the standpoin t of the Federal Reserve, these "credit" policies repre-
sen t a significant bre ak from tradition. In the po st w ar era, t he Fed scrupu-
lously avoid ed any exposure to private sector credit risk. How ever, in the
current crisis the central bank has acted to offset t he disruption of i n ter-
med iation by making imperfectly secured loan s to financial i nstitutions and
by lendin g directly to high g ra de non-finan cial borro wers. In a dd ition , the
fisca l auth ority acting in conjun ctio n w ith the c entral bank injected equity
into the major banks with the objective of improving credit flows. Though
the issue is not without considerable con trov ersy, many observ ers argue that
these interv entions helped stab ilized financial markets and, as consequence,
helped limit the dec line of real activit y. Since these policies are relatively
new, m uc h of the existing literature is silen t about them.
With th is backgroun d in m ind, we begin in the next section b y d eveloping
a baseline model that incorporates financial intermediation into an otherwise
frictionless business cycle f ram e work. O u r goal is twofold: first t o illustrate
how disruptions in financial interm ediation can induce a crisis that affects
real ac tiv ity; and seco nd , to illustrate how various credit market interv entions
b y th e central bank and th e Tr easury o f the type w e hav e seen recently, might
work to mitigate the crisis.
As in Bernanke and Gertler (1989), Kiyotaki and Moore (1997) and oth-
ers, we endogenize financial mark et frictions by in troducing an agency prob-
lem between borrowers and lenders.
2
The agency problem works to introduce
a wedge between the cost of external finance and the opportunity cost of in-

1
For a description of the disruption of financial intermediation during the current re-
cession, see Brunnermeier (2008), Gorton (2008) and Bernanke (2009). For a more general
description of financial crisis over the last several hundred years, see Reinhart and Rogoff
(2009).
2
A p artial of other m acro models with financial frictions in this vein includes,
Williamson (1987), Kehoe and Livene (1994), Holmstrom and Tirole (1997), Carlstrom
and Fuerst (1997), Caballero and Kristhnamurthy (2001), Kristhnamurthy (2003), Chris-
tiano, Motto and Rostagno (2005), Lorenzoni (2008), Fostel and Geanakoplos (2009), and
Brunnermeir and Sannikov (2009).
3
ternal finance, whic h adds to the overall cost of credit that a borrowe r faces.
Thesizeoftheexternalfinance premium, further, d epends on the c ondition
of borrower balance sheets. Roughly speaking, as a borrower’s percenta ge
stake in the outcom e of an investment project increases, his or her incen-
tiv e to deviate from the interests of lenders’ declines. The external finance
premium then d eclines as a result.
In general eq u ilib riu m, a "financial accelerator" em erges. As balance
sheets strengthen with impro ved econ om ics conditions, the external finance
problem declines, whic h works to enhance borrow er s pending, th us en ha ncing
the boom. Along the w a y, there is m utual feedback between the financial and
real sectors. In this framework, a crisis is a situation where balance sheets of
borrowers deteriorate sharply, possibly associated with a sharp deterioration
in a sset prices, causing the external finance premium to jum p. The im pact
of the financial distress on the cost of credit t hen depresses real activity.
3
Bernanke and Gertler (1989), Kiyotaki and Moore (1997) and others focus
on credit constraints faced by non-financial borrow ers.
4

As we noted earlier,
ho wever, the evidence suggests that disruption of financial intermediation is
a key feature of both recen t and histo rical crises. Thus w e focus our atten tion
here on financial interm ediation.
We begin by supposing that financial in termediaries hav e skills in evaluat-
ing and monitoring borrow ers, whic h makes it efficient for credit to flow from
lenders to non-financial borro wers through the in term ed iaries. In particular,
we a ssum e that households deposit fu n ds in financial intermediaries that in
turn lend funds to non-financial firm s. We then in troduce an agency problem
that poten tially constrains the ability of intermediaries to obtain funds from
depositors. When the constraint is binding (or there is s ome chance it may
bind), the intermediary’s balance sheet lim its i ts ability to ob ta in deposits.
In this instance, the con straint effectively in troduces a w edg e between the
loan and deposit rates. During a c risis, th is spread widens substan tially,
whichinturnsharplyraisesthecostofcreditthatnon-financial borro wers
face.
As recent ev ents suggest, ho wever, in a cr isis, fina ncial institu tion s face
3
Most of the models focus on the impact of borrower constraints on producer durable
spending. See Monacelli (2009) and Iacoviello (2005) for extensions to consumer durables
and housing. Jermann and Quadrini (2009), amongst others, focus on borrowing con-
straints on employment.
4
An exception is Holmstrom and Tirole (1997). More recent work includes see He and
Kristhnamurthy (2009), and Angeloni and Faia (2009).
4
difficu lty not only in obtaining depositor funds in retail financial m arkets
but a lso in obta ining f unds from one another in wholesale ("in ter-bank")
mar kets. Indeed, the first signals of a crisis are often strains in the in terbank
mar ket. We capture this phenom en on by subjecting financia l institutions to

idiosyncra tic "liquidity" shock s, whic h have the effect of creating surplus and
deficits of fun ds across financial institutions. If the in terbank market works
perfectly, then funds flow sm oothly from in stitu tion s w ith surp lus f unds to
those in need. In this case, loan rates are th us equalized across differen t
fin an cial institutions. Aggregate behavio r in this instance resembles the case
of homogeneous intermediaries.
However,totheextentthattheagencyproblemthatlimitsanintermedi-
ary’s ability to obtain f u nd s from depositors also lim its its ability to obtain
funds from other financial institutions and to the exten t that nonfinancial
firm s can obtain funds only from a limited set of financial interm ediaries,
disruptions of in ter-bank mark ets are possible that can affect real activit y.
In this instance, intermediaries w ith de ficit funds offer higher loan rates to
nonfinancial firms than intermediaries with surplus funds. In a crisis this gap
widens. Financial markets effectiv ely become segmen ted and sclerotic. A s
we show, the inefficien t allocation of funds across in termediaries can further
depress a ggregate activity.
In section 3 we incorporate credit policies w it hin the fo rm al framework.
In practice th e central bank emp loyed three b road types of policies. The first,
which was int roduced early i n the crisis, was to permit disc ount window lend-
ing to ban ks secured by private credit. The second, introduced in the wake
of the Lehmann default was to lend directly in relativ ely high grade credit
mar kets, including markets in commercia l paper, agency debt and mortga ge-
backed securities. The third (and m ost co ntro versial) in volv ed direct a ssis-
tance to large financial institutions, includin g the equity injections and debt
guarantees under the Troubled Assets Relief Program (TAR P) as w ell as the
emergency loans to JP Morgan Chase ( who t ook o ver Bear Stearns) and AIG.
We stress that within our framework, the net benefits from these various
credit market interven tions are increasing in the severity of t he crisis. This
helps account for wh y it makes sense to employ them only in crisis situations.
In section 4, we use the model to sim ulate numerically a crisis that has

some key features of the curren t crisis. Ab sent credit market frictions, the
disturban ce initiating the crisis induces only a mild recession. W ith credit
frictions (especially those in interb ank mark et), ho wev er , an endogenous dis-
ruption of financial intermediation w orks to magnify the downturn. We then
5
explore ho w various credit policies can help mitigate the situation.
Our baseline model is quite parsimonious and meant mainly to exposit
the key issues. In section 5, we discuss a number of qu estions and possible
extensions. In s o m e cases, we discuss a relevan t literature, stressin g the
implica tion s of this literature for going forw ard .
2 A Canonical Model of Financial I ntermedi-
ation and B usiness Fluctuations
Overall, the specific business cycle model is a h ybrid of Gertler and Karad i’s
(2009) f ram ework that allo ws for financial in term ediation a nd Kiy otaki and
Moore’s (2008) framework that allo w s for liquidity risk. We keep the core
macro model simple in order to see clearly the role of inter m ed iation and
liquidity. On the other hand, w e also allo w for some features prevalent in
con ventional qu antitativ e macro models ( such as Christiano, Eichen ba um
and Evans (2005), Smets and Wouters (2007)) in order to get rough sense of
theimportanceofthefactorsweintroduce.
5
For simplicit y we restrict atten tion to a purely real model and only credit
policies, as opposed to conven tion al moneta ry models. Extending the model
to allo w for nom inal rigidities is s traightforw ard (see., e.g., G ertler and
Karadi, 2 009), and permits study ing conv entional monetary policy along
with uncon ventional po licies. Ho wev er, because much of the insight in to how
credit market frictions ma y a ffect real activity and ho w various credit policies
may work can be obtained from studying a purely real model, we abstract
from nominal f rictions.
6

5
Some recent monetary DSGE models that incorporate financial factors include Chris-
tiano, Motto, and Rostagno (2009) and Gilchrist, Ortiz and Zakresjek (2009).
6
There, however, several i nsights that monetary models add, however. First, if the
zero lo wer bound on the nominal interest is binding, the financial market disruptions will
have a larger effect than otherwise. This is because the central bank is not free to further
reduce the nominal rate to offset the crisis. Second, to the extent there are nominal price
and/or wage rigidities that induce countercyclical markups, the effect of the credit market
disruption and aggregate activity is amplified. See, e.g., Gertler and Karadi (2009) and
Del Negro, Ferrero, Eggertsson and Kiyotaki (2010) for a n illustration of both of these
points.
6
2.1 Physical S etup
Befor e describing our economy with financial frictions, w e present the phy s-
ical en vironm ent.
There are a con tin uu m of firmsofmassunitylocatedonacontinuum
of islands. Each firm produces output using an identical constant returns
to scale Cobb-Douglas production function with capital and labor as inputs.
Cap ital is not mob ile, but labor is perfectly mob ile across firms and islands.
Because labor is perfectly mobile, we can express aggregate output Y
t
as a
function of aggregate capital K
t
and aggregate labor hours L
t
as:
Y
t

= A
t
K
t
α
L
1−α
t
, 0 <α<1, (1)
where A
t
is aggregate productivit y which follow s a Markov process.
Eac h period in vestment opportunities arrive randomly to a fraction π
i
of
islands. On a fraction π
n
=1− π
i
of islands, there are no investment op-
portunities. Only firm s on islands with in vestment opportunities can acquire
new capital. The arrival of investment opportunities is i.i.d. across time and
across islands. The structure of this idiosyncratic risk pro vides a simple w ay
to introduce liquidity ne eds by firms, follo wing Ki y otaki and Moore (2008).
Let I
t
denote aggregate in vestmen t, δ the rate of physical deprecation and
ψ
t+1
a shock to the qualit y of capital. Then the law of m o tion for capital is

given by :
K
t+1
= ψ
t+1
[I
t
+ π
i
(1 − δ)K
t
]+ψ
t+1
π
n
(1 − δ)K
t
= ψ
t+1
[I
t
+(1− δ)K
t
]. (2)
The first term of the righ t reflects capital accumulated by firms on in vesting
islands and the second is capital that remains on non-investing islands, after
depreciation. Summ ing across i sland s yields a con ven tion al aggregate relation
for the evolu tion of c ap ital, except for the presence of th e disturbance ψ
t+1
,

which w e refer to as a capital quality shock. Follo wing the finance literature
(e.g., Merton (1973)), w e introduce the capital quality shock as a simple w ay
to introduce an exogenous source of variation in the value of capital. As will
become cl ear later, the mark et price o f capital wi ll be e ndogenous within
our framew ork. In this regard, the capital qual it y shock will s erve as a n
exogenous trigger of asset price dynamics. The random variable ψ
t+1
is best
thought of as cap turing some form o f economic o bsolescence, as opposed t o
7
ph ysical depreciation.
7
We assume the capital qualit y shock ψ
t+1
also follo w s
a Marko v process.
8
Firms on inv estin g islands acqu ire cap ital from capital good s pr oducers
who operate in a national market. There are con vex adjustment costs in the
gross rate of c hange in investmen t for capital goods producers. Aggregate
output is divided between household consumption C
t
, in vestmen t expendi-
tures, and go vernment consumption G
t
,
Y
t
= C
t

+[1+f(
I
t
I
t−1
)]I
t
+ G
t
(3)
where f(
I
t
I
t−1
)I
t
reflects physical adjustment costs, with f(1) = f
0
(1) = 0 and
f
00
(I
t
/I
t−1
) > 0. Thus the aggregate production function of capital goods
producers is decreasing returns to scale in the short-run and is constan t
returns to scale in the long-run.
Next we turn to preferences:

E
t
∞
X
i=0
β
i
∙
ln(C
t+i
− γC
t+i−1
) −
χ
1+ε
L
1+ε
t+i
¸
(4)
where E
t
is th e expectation operator conditional on date t information and
γ ∈ (0, 1). We abstract from many f rictions in the conventional DSGE frame-
work (e.g. n om in al price a nd w a ge rigidities, variable capital u t ilization,
etc.). Howev er, we allo w both habit formation of consumption and adjust-
ment costs o f inv estment because, as th e DSGE literatu re has found, these
features a r e h elp ful for reasonable quantita tive performance an d because they
can be kept in the model at minimal cost of additional complexity.
If there were no financial frictions, the competitiv e equilibrium w o uld

correspond to a solution of the planner’s problem that involv es choosing ag-
gregate quantities (Y
t
,L
t
,C
t
,I
t
,K
t+1
) as a function of the aggregate state
7
One w ay to motivate this disturbance is to assume that final output is a C.E.S. com-
posite of a continuum of intermediate goods that are in turn produced by employing
capital and labor in a Cobb-Douglas production technology. Suppose that, once capital is
installed, capital is good-specific and that eac h period a random fraction of goods become
obsolete and are replaced b y new goods. The capital used to produced the obsolete goods
is now worthless and the capital for the n ew goods is not fully on line. The aggregate
capital stock will then evolve according to equation. (2).
8
Other recent papers that mak e use of this kind of disturbance include, Gertler and
Karadi (2009), Brunnermeier and Sannikov (2009) and Gourio (2009).
8
(C
t−1
,I
t−1
,K
t

,A
t
,ψ
t
) in order to maximize th e expected discou nted utility
of the represen tative household subject to the resource c o nstraints. This
frictionless econo my (a standard real busin ess cycle model) will serve as a
benchmark to w hic h we may compare the im plications of the financial fric-
tions.
In what follow s w e will introduce banks that intermediate funds between
households and non-financial firms i n a retail financial m arket. I n addition,
we will allo w for a wholesale in ter-ba n k market, where banks with surplus
funds on non-inv estment islands lend to banks in need o f funds on i n vesting
islands. We will also in troduce financial frictions that ma y impede credit
flowsinboththeretailandwholesalefinancial mark ets and then study the
consequences for real activit y.
2.2 Households
In our econom y with c redit frictions, households lend t o no n-financial firms
via fin ancial in term e diaries. Following Gertler and Karad i (2009), w e formu -
late the household sector in way that permits maintaining the tractability of
the representative agen t approac h.
In particular, t here is a representative household with a continuum of
members of measure unit y. Within the household there are 1 − f "w ork-
ers" and f "bankers". Work ers supply labor and return their wages to the
household. Each banker manages a fin an cial in ter m ed iary (which we will call
a "bank") and transfers nonnegativ e dividends bac k to household subject to
its flow of fund constraint. Within the f am ily there i s perfect consumption
insurance.
Households do not hold capital directly. Rather, they deposit funds in
banks. (It may be best t o think o f them as d epositing f unds in banks other

than the ones they ow n ). In our model, bank deposits are riskless one period
securities. Households may also hold riskless one period government debt
which is a perfect substitute for bank deposits.
Let W
t
denote the wage rate, T
t
lump sum taxes, R
t
the gross return
on riskless debt from t − 1 to t, D
ht
the quantity of riskless debt held, a nd
Π
t
net distributions from o w nership of both banks and non-financial firms.
Then t he h ousehold chooses consumption, labor supply a nd ri skless debt
(C
t
,L
t
,D
ht+1
) to maximize expected discoun ted utility (4) subject to t he
flow of f unds constrain t,
9
C
t
= W
t

L
t
+ Π
t
− T
t
+ R
t
D
ht
− D
ht+1
. (5)
Let u
Ct
denote the marg ina l utilit y of consump tion and Λ
t,t+1
the house-
hold’s stoc h astic discoun t factor. Then the househo ld’s first order conditions
for labor supply and consumption/sa ving are given by
E
t
u
Ct
W
t
= χL
ϕ
t
, (6)

E
t
Λ
t,t+1
R
t+1
=1, (7)
with
u
Ct
≡ (C
t
− γC
t−1
)
−1
− βγ(C
t+1
− γC
t
)
−1
and
Λ
t,t+1
≡ β
u
Ct+1
u
Ct

.
Because b a nks may be financially constrained, bankers will reta in earn-
ings to accum ulate assets. Absent some motiv e for pa ying dividends, they
may find it optimal to accumulate to the point where the financial constraint
they face is no longer binding. In o rder to limit bankers’ abilit y to sa ve to
overcome fina ncial constraints, w e allo w for turn over between bankers and
w ork ers. In particular, w e assume that with i.i.d. probabilit y 1 − σ, a bank er
exits next period, (which gives an av erage survival time =
1
1−σ
). Upon ex-
iting, a banker transfers retained earnings to the household and becom es
a w or ker. Note that the expected survival time ma y be quite long (in our
baseline calibration it is ten y ear s.) It is critical, ho wever, that the expected
horizon is finite, in order to motivate pa youts while the financial c onstrain ts
are still binding.
Each period, (1 − σ)f w o rkers randomly become bank ers, keeping the
num ber in each occup atio n constan t. Finally, because in equ ilibrium bankers
willnotbeabletooperatewithoutanyfinancial resources, each new bank er
receiv es a "start up" transfer from the family as a small constant fraction
of the total assets of entrepreneurs. Accordingly, Π
t
is net funds transferred
to the household:i.e., funds transferred from exiting bankers min us the funds
transferred to new bankers ( a side from small profits of capital producers).
An alternativ e to our ap proach of having a consolidated f am ily of work-
ers and bankers would be to hav e the two groups as di stinct sets of agents,
without any consumption i nsurance bet ween the two groups. It is unlikely,
however, that the key results of our paper would change qualitatively. By
10

sticking with c omplete consum ptio n in su ran ce, we are ab le to have le nd ing
and borro w in g in equilibrium and still maintain tractabilit y of the represen-
tative household a pproach.
2.3 Banks
To finance lending in each period , banks raise funds in a national financial
mark et. Within the national financial market, there is a retail market, where
banks obtain deposits from hou seholds; and a wholesale market, where bank s
borro ws and lend amongst one and anot her.
At the beginning of the period each ban k raises deposits d
t
from house-
holds i n the retail financialmarketatthedepositrateR
t+1
. After the retai l
fin an cial mark et closes, in vestment opportunities for non financial firms ar-
riv e random ly to di fferen t islands. Banks can only make loans to nonfinancial
firm s located on the same island. As we stated earlier, for a fraction π
i
of
locations, new in vestment opportunities are available to finance as w ell as
existing projects. Conversely, for a fraction π
n
=1− π
i
,nonewinvestments
areavailabletofinance, only existing ones. On the in terb ank market, banks
on islands with new lending opportunities will borrow funds from those on
islands with no new project arrivals.
9
Financial frictions affect real activity in our framew ork via the impact

on funds a vailable to banks. For simplicit y, ho wever, there is no friction
in transferring funds between a bank and non-financial firms in the same
island. In particular, we suppose that the bank is efficientatevaluating
and monitoring non-financial firms o f the same island, and also at enforcing
con tr actu al obligations with these borrowers. We assume the costs to a bank
of performing these activities are negligible. Accord ingly, giv en its supply of
available funds, a bank can lend frictionlessly to non-financial firms of the
same island against their future profits. In this regard, firms are able to offer
banks perfectly state-contingent debt. It is simplest to think of the bank’s
claim on nonfinancial firmsasequity.
9
Our model is thus one where liquidity problems emerge in part due to limited mark et
participation, in the spirit of Allen and Gale (1995, 2007) and others. This is because
within our framework (i) only banks of the same island can make loans to nonfinancial
firms and (ii) banks on investing islands cannot raise additional funds in the retail financial
market after they learn their customers have investment opportunities.
11
After learning about its lending opportunities, a bank decides the vol-
ume of loans s
h
t
to m ake to non-financial firms a nd the volume of in terbank
borro wing b
h
t
where the superscript h = i, n denotes the island t ype (i for
investin g a n d n f or n on-inv esting) on which the b ank is located during the
period. Let Q
h
t

be price o f a loan (or " asset" ) - i.e. the mark et price of the
bank’s claim on the future returns from one unit of present capital of non-
financial firm at the end of period. We index t h e asset price by h because,
o w in g t o t em poral ma rket segmentation, Q
h
t
maydependonthevolumeof
opportunities t hat the ba nk faces.
For an i ndiv idual bank, the flow-of-funds constraint im plies the value of
loans fu nd ed within a given period, Q
h
t
s
h
t
,mustequalthesumofthebank
net worth n
h
t
, its borrowings on t he interbank market b
h
t
and deposits d
t
:
Q
h
t
s
h

t
= n
h
t
+ b
h
t
+ d
t
. (8)
Note that d
t
does not depend upon the volume of the lending opportunities,
which is not realized at the time of obtaining deposits.
Let R
bt
be the in terban k interest rate from periods t−1 to period t.Then
net worth at t is the gross payoff from assets funded at t − 1,netborrowing
costs, as follo w s:
n
h
t
=[Z
t
+(1− δ)Q
h
t
]ψ
t
s

t−1
− R
bt
b
t−1
− R
t
d
t−1
, (9)
where Z
t
is the dividend pa yment at t on the loans t he bank funds at t − 1.
(Recall that ψ
t
is an exogenous aggregate shoc k to the qualit y of capital).
Observethatthegrosspayoff from assets depends on the location specific
asset price Q
h
t
,whichisthereasonn
h
t
depends on t he realization of the
location specificshockatt.
Giv en that the bank pays dividends only when it exits (whic h occurs with
a consta nt probability), the objective o f the b an k a t th e en d of period t is
the expected present value of future dividends, as follow s
V
t

= E
t
∞
X
i=1
(1 − σ)σ
i−1
Λ
t,t+i
n
h
t+i
, (10)
where Λ
t,t+i
is the stoc h astic discount factor, whic h is equal to the margina l
rate of substitution between consumption of date t + i and d ate t of the
representativ e household.
In order to maintain tractability, we make assumptions to ensure that
we do not ha ve to k eep trac k of the distribution of net w orth across islands.
12
In particular, we allow for arbitrage at t h e beginning of each period (before
investment opportunities arriv e) to e nsure that e x ante expected rates of
return to interm ed iation are equal across island s. In particular, we sup pose
that a fraction of banks on islands where expected returns are low can move
to islands where they are high. Before they mo ve, they sell their existing
loans to n on financial firms t o t he oth er banks that rema in on the island in
exchange for inter-b ank loans that the remaining banks have been holding in
their portfolios. T hese tr an sactions keep eac h existing loan to nonfinancial
firms on the island it w a s initiated. A t the same time, they permit arbitrage

to equalize returns across markets ex ante.
As will become clear later, ex a nte expected retu rns bein g equalized across
islands requires that the ratio of total interm ed iary net wor th to total capital
on each island be the same at t he beginning of each period
10
.Thus,given
this arbitrage activity and giv en that the liq u idity sh oc k is i.i.d., we do not
have to k eep track of the beginning of period distribution of net worth across
islands.
To motivate an endogenous constraint on the b a nk ’s ability to obtain
funds in either the retail or wholesale financial markets, we introduce the
follo w ing simple agency problem: We assume that after an bank o b tains
funds, the bank er managing the b ank may tra nsfer a fraction θ of "div ertable"
assets to his o r her family. D ivertable a ssets consists of total gross assets Q
h
t
s
h
t
net a fraction ω of in terbank borrowing b
h
t
. If a bank diverts assets for its
personal gain, it defaults on its debt and is shut do wn. The c reditors ma y
re-claim the rem ain ing fractio n 1− θ of funds. Because its creditors recognize
the bank’s incen tive to divert funds, they will restrict the amount they lend.
In this w ay a borro wing constraint ma y arise.
We allow for the possibilit y that bank ma y be constrained not only in
obtaining funds from depositors but also in obtaining funds from other banks.
Tho ugh w e permit the tigh tness of the constraint faced in each market to

differ. In particular, the parameter ω indexes (inversely) the relative degree
of friction in the in terb an k mark e t:
With ω =1, banks cannot divert assets financed by borro wing from other
banks: Lending b anks are able t o perfectly recover the assets that underlie the
loans th ey make. In this ca se, the interbank market o perates frictionlessly,
10
In turn, this requires a movement of net worth from low return to high return islands
that is equal in total to the quantity of interbank loans issued in the previous period. The
asset exchange between moving and staying banks described in the text accomplishes this
arbitrage.
13
and banks are not constrained in borrowing from one another. They ma y
only be c onstrained in obtaining funds from depositors.
In contrast, with ω =0, lending banks are no m ore efficient than depos-
itors in recovering assets from borrowing banks. In this case, the friction
that constrains a banks abilit y to o btaining funds on the in terbank mark et
isthesameasfortheretailfinancial mark et. In general, we can allow para-
meter ω to differ for borrow ing v e rsus lending banks. However, maintaining
symmetry simplifies the a nalysis w ithout affecting the main results.
We assume that the banker’s decision over whether to div ert funds must
be made at the end of the period after the realization of the idiosyncratic
uncertaint y that determin es its type, but before the realization of aggregate
uncerta int y in the follo w in g period. Here the idea is that if th e b an ker
is going to divert funds, it takes tim e to position assets and this must be
done be t ween the periods (e.g., during the nigh t). Let V
t
(s
h
t
,b

h
t
,d
t
) be the
maximized value of V
t
, given a n asset and liability configuration
¡
s
h
t
,b
h
t
,d
t
¢
at the end of period t. Then in order to ensure the bank does not div ert
funds, the follo w in g incentive constrain t m u st hold for each bank type:
V
t
(s
h
t
,b
h
t
,d
t

) ≥ θ(Q
h
t
s
h
t
− ωb
h
t
). (11)
In general the value of the bank at the end of period t − 1 satisfies the
Bellman e quation
V
t−1
(s
t−1
,b
t−1
,d
t−1
)
= E
t−1
Λ
t−1,t
X
h=i,n
π
h
{(1 − σ)n

h
t
+ σMax
d
t
[Max
s
h
t
,b
h
t
V
t
(s
h
t
,b
h
t
,d
t
)]}. (12)
Note that the loans and in terbank borrow ing are chosen after a shoc k to the
loan opportunity is realized while deposits are c h ose n before.
To solv e the decision problem, w e first guess that the value function is
linear:
V
t
(s

h
t
,b
h
t
,d
t
)=ν
st
s
h
t
− ν
bt
b
h
t
− ν
t
d
t
(13)
where ν
st
,ν
bt
and ν
t
are time varying parame ters, and verify this guess later.
Note that ν

st
is the marginal value of assets at the end of period t; ν
bt
is the
marginal cost of i nterbank d ebt; and ν
t
is the marginal cost o f deposits.
11
11
The parameters in the conjectured value function are independent of the individual
bank’s type because the value function is measured after the bank finishes its transaction
for the current this period and because the shock to the loan opportunity is i.i.d. across
periods.
14
Let λ
h
t
be the Lag rang ian multiplier for th e incentiv e constraint (11) faced
b y bank of type h and
λ
t
≡
P
h=i,n
π
h
λ
h
t
be the a verage of this multiplier across

states. Then giv en the conjectured form of th e value fu nction , we m ay express
the first order conditions for d
t
, s
h
t
,andλ
h
t
,as:
(ν
bt
− ν
t
)(1+λ
t
)=θωλ
t
, (14)
µ
ν
st
Q
h
t
− ν
bt
¶
(1 + λ
h

t
)=λ
h
t
θ(1 − ω), (15)
[θ − (
ν
st
Q
h
t
− ν
t
)]Q
h
t
s
h
t
− [θω − (ν
bt
− ν
t
)]b
h
t
≤ ν
t
n
h

t
. (16)
According to equation (14), the marginal cost of interbank bo rro wing ex-
ceeds the margina l cost of deposit if and only if the incentiv e constraint is
expected to bind for some state (
λ
t
> 0)andtheinter-bankmarketoperates
more efficiently than the retail deposit mark et (i.e., ω>0, meaning that as-
sets financed b y in terbank borro wing are harder to div ert than those financed
b y deposits). Equation (15) states that the marginal value of assets in terms
of goods
ν
st
Q
h
t
exceeds the marginal cost of interbank borrowing by banks on
type h island to the extent that the incentive constraint i s binding (λ
h
t
> 0)
andthereisafrictionininterbankmarket(ω<1). Finally, equation (16) is
the incentive co nstraint. It requires t hat the values of the bank’s net worth
(or equity capita l), ν
t
n
h
t
,mustbeatleastaslargeasweightedmeasureof

assets Q
h
t
s
h
t
net of interbank borrowing b
h
t
that a bank holds. In this w ay,
the agency problem introduces an endogenous balance sheet constraint on
banks.
The model for the general case with 0 ≤ ω ≤ 1 is somew ha t cumbersome
to so lve. There are, however, t wo interesting special cases that provide i nsight
in to the models w or kings. In case 1, there is a perfect in terba nk market,
which arises when ω =1. In case 2, the frictions in the in terb ank market are
of the same magn itude as in th e retail financial market, whic h arises when
ω =0. We next proceed to characterize each of the cases. The Ap pendix
then pro vides a solution for the general case of an interbank friction with
ω<1.
15
2.3.1 Case 1: Frictionless wholesale financial m ark et (ω =1)
If b an ks cannot divert assets financed by in ter-bank borrowing (ω =1), in-
terbank len ding is frictionless. As equation (15) sug gests, perfect arbitrage
in the interbank market equalizes the shado w values of assets in each market,
imply ing
ν
st
Q
b

t
=
ν
st
Q
l
t
, wh ich in turn implies Q
b
t
= Q
l
t
= Q
t
. T h e perfect inter-
bank m arket, further, implies th at the marginal value of assets in terms of
goods
ν
st
Q
t
must equal the marginal cost of borro win g on the in terba nk market
ν
bt
,
ν
st
Q
t

= ν
bt
. (17)
Because asset prices are equal across islan d types, we can drop the h
superscript in this case. Accordin gly, let μ
t
denote the excess value of a unit
of assets relative to deposits, i.e., the marginal value of holding assets
ν
st
Q
t
net
the marginal cost o f d eposits ν
t
. Then, giv en that banks are constrained in
the retail deposit market, equations ( 14) and ( 15) imply that the
μ
t
≡
ν
st
Q
t
− ν
t
> 0. (18)
It follows that the incentive constrain t (16) in this case may expressed as
Q
t

s
t
− b
t
= φ
t
n
t
(19)
with
φ
t
=
ν
t
θ − μ
t
. (20)
Note that since in ter bank borrowing is f rictio nless, the c o n straint applies to
assets in ter m ediated min u s in terb ank borro w ing. How tightly the constraint
binds depends positively on the fraction of net assets the bank can divert
and negatively on the excess value of bank assets, give n by μ
t
. The higher
the excess v alue is, the greater is the franc hise value of the bank and the less
likely it is to divert funds.
Let Ω
t+1
be the marginal value of net worth a t date t+1 and let R
kt+1

is
the gross rate of r eturn o n ba n k assets. Then after combining the conjectured
valuefunctionwiththeBellmanequation,wecanverifythevaluefunction
is linear in
¡
s
h
t
,b
h
t
,d
t
¢
if μ
t
and ν
t
satisfy:
ν
t
= E
t
Λ
t,t+1
Ω
t+1
R
t+1
(21)

16
μ
t
= E
t
Λ
t,t+1
Ω
t+1
(R
kt+1
− R
t+1
) (22)
with
Ω
t+1
=1− σ + σ(ν
t+1
+ φ
t+1
μ
t+1
), and
R
kt+1
= ψ
t+1
Z
t+1

+(1− δ)Q
t+1
Q
t
.
Let us define the "a ugm ented stoc ha stic discount factor" as the stoc hastic
discount factor Λ
t,t+1
w eigh ted by t he (stochastic) m arginal value of net w orth
Ω
t+1
. (The margina l value of net worth is a we ighted average of margina l
values f or exiting and for contin uing banks. If a c ontinuing bank h as an
additiona l net w or th, it can save the cost of deposits and can increase assets
b y the leverage ratio φ
t+1
, where assets hav e an excess value equal to μ
t+1
per unit). A cco rding to (21), the cost of deposits per unit to the bank ν
t
is the expected product of the augmen ted stochastic discount factor and the
deposit rate R
t+1
. Similarly from (22), the excess value of assets per unit, μ
t
,
is the expected product of the augmen ted stochastic discount factor and the
excess return R
kt+1
− R

t+1
.
Since the leve rage ratio net of in terbank borrow ing, φ
t
, is independen t
of both bank-specific factors and island-specificfactors,wecansumacross
individual banks t o obtain the relation for the demand for total bank assets
Q
t
S
t
as a function o f total net w orth N
t
as:
Q
t
S
t
= φ
t
N
t
(23)
where φ
t
is given b y e qua tion ( 2 0). Ov erall, a setting with a perfect interb ank
is isomorph ic to one wh ere banks do not face idiosyncratic liquidity risks.
Aggrega te bank lending is simply constrained b y aggregate bank capital.
If the banks’ balance sheet constraints are binding in the retail financial
mar ket, there will be excess returns on a ssets over deposits. H owever, a

perfect in terba nk m arket leads to arbitrage in returns to assets across mark e t
as follows:
E
t
Λ
t,t+1
Ω
t+1
R
kt+1
= E
t
Λ
t,t+1
Ω
t+1
R
bt+1
>E
t
Λ
t,t+1
Ω
t+1
R
t+1
. (24)
As will become clear, a crisis in suc h econom y is associated with an increase
in the excess return on assets for banks of all types.
17

2.3.2 Case 2: Symmetric frictions in whole sale and retail financial
mark ets (ω =0)
In this instance the bank’s abilit y to div ert funds is independent of whether
the funds a re obtained in ei ther the retail or whol esale financial mark ets. This
effectively makes the borrowing constraint the bank faces sym metric in the
t wo credit mark ets. As a consequence, interb ank loans and deposits become
perfect substitutes as sou rces of finance. Accordingly, equation (14) implies
that the marginal cost of interbank bo rro wing is equal to the m arginal c ost
of deposits
ν
bt
= ν
t
. (25)
Here, eve n if banks on in vesting islands are financially constrained, banks on
non-investing islands ma y or may not be. Roughly speaking, if the constrain t
on inter-b ank borrowing binds tightly, banks in non-in vesting islands will be
mor e inclined to use t h eir funds to re-finance existing investmen ts rather
than lend them to banks on investin g islands. This raises the likelih ood that
banks on non-in vesting islands will earn zero excess returns on their assets.
Because asset supply per unit of bank net w orth is larger on investing
islands than on non-in vesting islands, the asset price is low er, i.e., Q
i
t
<Q
n
t
.
Intuitively, given that the leverage ratio constraint limits banks’ ability to
acquire assets, prices will clear at lo wer values on investing islands where

supplies per unit of bank net worth are greater. In the previous case of a
perfect interbank mark et, funds flow from non-inv esting to investing islands
to equalize asset prices. Here, frictions in the in ter-ban k mark et limit the
degree of arbitrage, k eeping Q
i
t
below Q
n
t
.
A lower asset price on the i nv esting island, of co ur se, means a higher
expected return. Let μ
h
t
≡
ν
st
Q
h
t
− ν
t
be the excess value of assets on a type h
island. Then we ha ve:
μ
i
t
>μ
n
t

≥ 0. (26)
The positiv e excess return implies that banks in the investing islands are
finance c onstrained. T h u s t he l ev erage ratios for b anks on eac h island type
are given b y:
Q
i
t
s
i
t
n
i
t
= φ
i
t
=
ν
t
θ − μ
i
t
(27)
Q
n
t
s
n
t
n

n
t
≤ φ
n
t
=
ν
t
θ − μ
n
t
, and
µ
Q
n
t
s
n
t
n
n
t
− φ
n
t
¶
μ
n
t
=0. (28)

18
In this case the method of undetermined coefficients yields
ν
t
= E
t
Λ
t,t+1
X
h
0
=i,n
π
h
0
Ω
h
0
t+1
R
t+1
= E
t
h
0
Λ
t,t+1
Ω
h
0

t+1
R
t+1
(29)
μ
h
t
= E
t
h
0
Λ
t,t+1
Ω
h
0
t+1
(R
hh
0
kt+1
− R
t+1
) (30)
with
Ω
h
0
t+1
=1− σ + σ(ν

t+1
+ φ
h
0
t+1
μ
h
0
t+1
), and
R
hh
0
kt+1
= ψ
t+1
Z
t+1
+(1− δ)Q
h
0
t+1
Q
h
t
.
With an imperfect in terbank market, both the marginal value o f n et worth
Ω
h
0

t+1
and the return on assets R
hh
0
kt+1
depend on which island type a bank
en ters in the sub sequent period. Accordingly, we ind ex eac h b y h
0
and t ak e
expectations over h
0
conditio nal on date t informa tion denoted as E
t
h
0
.
Because levera ge ratios differ across islands, w e aggregate separately a cro ss
bank-types to obtain the aggregate relations:
Q
i
t
S
i
t
= φ
i
t
N
i
t

(31)
Q
n
t
S
n
t
≤ φ
n
t
N
n
t
, and (Q
n
t
S
n
t
− φ
n
t
N
n
t
) μ
n
t
=0, (32)
where φ

i
t
and φ
n
t
are g iven b y equations (27) a nd (2 8). As we will see,
in the general equilibrium, investm ent will depend on the price of capital
on "investing" islands, Q
i
t
. A ccordin gly, it is the aggregate balance sheet
constraint on asset demand for banks on investing islands, given by equation
(31) that becom es c ritical fo r interaction s bet ween financial conditions and
production.
Next,from(25,26,29,30),welearnthatthereturnsobey
E
t
h
0
Λ
t,t+1
Ω
h
0
t+1
R
ih
0
kt+1
>E

t
h
0
Λ
t,t+1
Ω
h
0
t+1
R
nh
0
kt+1
(33)
≥ E
t
h
0
Λ
t,t+1
Ω
h
0
t+1
R
bt+1
= E
t
h
0

Λ
t,t+1
Ω
h
0
t+1
R
t+1
.
with ≥ holds with str ict inequ ality iff μ
n
t
> 0 and holds with equalit y iff
μ
n
t
=0. With an imperfect in ter-ban k mar ket, a crisis is associated with
both a rise in t h e excess return for banks on investing islands a n d in crease
in the dispersion of returns between island types.
19
As w e sho w in Appendix, for the case where the interbank market is im-
perfect but operates with less friction than the retail deposit market (i.e.,
0 <ω<1), the interbank rate w ill lie between the retu rn on loa n s and the
deposit rates. Intuitively, because a dollar interbank credit will tighten the
incentiv e constraint b y less than a dollar of deposits (since lending banks
are able to recover a greater fraction of creditor assets than are depositors),
the interba nk rate exceeds the deposit rate. Howe ver, because lending banks
are not able to perfectly recover assets ω<1, there is still imperfect arbi-
trage which keeps the expected discoun ted interbank rate below the expected
discounted return to loans.

2.4 Evolution of Bank Net Worth
Lettotalnetworthfortypehbanks,N
h
t
, equal the sum of the net wo rth of
existing entrepreneurs N
h
ot
(o for old) and of en tering en trepreneurs N
h
yt
(y
for young):
N
h
t
= N
h
ot
+ N
h
yt
. (34)
Net worth of e xisting entrepreneurs equals e arnings o n assets net debt pay-
ments made in the previous period, m ultiplied by the fraction th a t survive
un til the current period , σ:
N
h
ot
= σπ

h
{[Z
t
+(1− δ)Q
h
t
]ψ
t
S
t−1
− R
t
D
t−1
}. (35)
Because the arrival of in v estmen t opportunity is independent across time,
the interbank loa ns a r e net ou t in the aggreg ate h ere. We assume that the
family transfers to eac h new banker is the fraction ξ/(1−σ) of the total value
assets of exiting en trepreneurs, implying:
N
h
yt
= ξ[Z
t
+(1− δ)Q
h
t
]ψ
t
S

t−1
. (36)
Finally, b y the balance-sheet of the entire banking sector, deposits equal the
difference between total assets and bank net w o rth as follow s,
D
t
=
X
h=i,n
(Q
h
t
S
h
t
− N
h
t
). (37)
Observe that the ev o lution of net worth depends fluctuations in the r etur n
to assets Further, the higher the l everage of t he bank is, the larger will be
20
the percentage impact of return fluctuations on net w orth. Note also that a
deteriora tion of cap ita l quality (a d e clin e in ψ
t
) directly reduces n et worth.
As we will show , there will also be a second round effect, as the decline in net
w orth induces a fire sale of assets, depressing asset prices and thus further
depressing bank net worth.
2.5 Nonfinancial F irms

There are two t ypes of non-financial firms: goods producers and capital pro-
ducers.
2.5.1 Goods Producer
Com petitiv e goods producers on differen t islands operate a constant returns
to scale tech nolog y with capital and la bor i np uts, given by e qua tion (1).
Since labor is perfectly mobile across islands, firms ch oose labor to satisfy
W
t
=(1− α)
Y
t
L
t
(38)
It follo ws that w e ma y express gross profits per unit of capital Z
t
as follow s:
Z
t
=
Y
t
− W
t
L
t
K
t
= αA
t

µ
L
t
K
t
¶
1−α
. (39)
As w e noted earlier, conditional on obtaining funds from a bank, a goods
producer does not face an y further financial frictions and can comm it to pa y
all the future gross p rofits to the creditor bank. A good s p roducer with a n
opportunit y to in vest obtains funds from an interm ed iary b y issuing new
state-con t ingent securities (equity) at the price Q
i
t
. The producer then uses
the funds to buy new capital goods from capital good s producers. Each unit
of equity is a state-contingent claim to the future returns from one unit of
investment:
ψ
t+1
Z
t+1
, (1 − δ)ψ
t+1
ψ
t+2
Z
t+2
, (1 − δ)

2
ψ
t+1
ψ
t+2
ψ
t+3
Z
t+3
, .
Throug h perfect competition, the price of new c apital goods i s equal to Q
i
t
,
andgoodsproducersearnzeroprofits state-by-state.
Note that giv en constant returns and perfect labor m obility, w e do not
have k eep track of the distribution of ca pita l across islands. As in the stan-
dard competitiv e model with constan t returns, the size distribution of firms
is indeterm inate.
21
2.6 Capital Goods Producers
Capital producers o perate in a national m ark et. They make ne w capital
using input of fin al output and subject to adjustment costs, as described in
section 2.2. They sell new capital t o firms on investin g islands at t h e price
Q
i
t
. Giv en that households o wn capital producers, the objective of a capital
producer is to c h oose I
t

to solve:
max E
t
∞
X
τ=t
Λ
t,τ
½
Q
i
τ
I
τ
−
∙
1+f
µ
I
τ
I
τ−1
¶¸
I
τ
¾
From profitmaximization,thepriceofcapitalgoodsisequaltothemarginal
cost of investm ent goods production as follows,
Q
i

t
=1+f
µ
I
t
I
t−1
¶
+
I
t
I
t−1
f
0
(
I
t
I
t−1
) − E
t
Λ
t,t+1
(
I
t+1
I
t
)

2
f
0
(
I
t+1
I
t
) (40)
Profits (which arise only outside of steady state), are redistributed lump sum
to households.
2.7 Equ ilib r ium
To close the model (in the case without government policy), w e require mar-
ket clearing in both the market for securities and the labor ma rket. Total
securities issued on in vesting and non-investing islands correspond to aggre-
gate capital acquired by each t ype, as follow s:
S
i
t
= I
t
+(1− δ) π
i
K
t
(41)
S
n
t
=(1− δ) π

n
K
t
.
Note that demand for secu rities b y banks is given by equation (23) in the
case of a frictionless in terbank market and by equations (31) and (32) in the
case of an imperfect interb ank market. Observ e first that the market price of
capitaloneachislandtypewillingeneraldependonthefinancial condition
of the associated banks. Second, with an imperfect interbank m arket, the
asset p rice will be gen erally lower (or, equivalen tly,state-co ntingent loans
rates offered by banks will be generally greater) on in vesting islands than
elsewhere.
12
12
This verifies the earlier conjecture in Section 2.3.2. For the more general case of
imperfect interbank market, see Appendix 1.
22
Finally, the condition t hat labor de mand equals l abor s upply requires
that
(1 − α)
Y
t
L
t
· E
t
u
Ct
= χL
ϕ

t
(42)
Because of Walras’ Law, once the market for goods, labor, securities, and
interbank loans is cleared, the market for ri skless debt will be cleared auto-
matically:
D
ht
= D
t
+ D
gt
,
where D
gt
is supp ly o f g ov ernm ent debt. T his co m p letes t he description of
the model.
Absent credit market frictions, the model reduces to a real business cycle
framework modified with habit formation and flow in vestment adjustme nt
costs. W ith the credit market frictions, ho wev er, balance sheet constraints
on banks ability to obta in funds in retail and wholesale market may limit
real investm ent spending, affecting agg reg ate real a ctivity. As we will show, a
crisis is possible w here weakening of bank balance sh eets significantly disru p ts
credit flo w s, depressing real activity.
As we have discussed, one exam ple of a factor that could w eaken bank
balance sheets is a deterioration of the underlying quality o f capital. A
negativ e qualit y shock directly reduc es t he value of bank net worth, forcing
banks to reduce asset holding s. A second round effect on bank net w o rth
arises as the fire sale of assets reduces th e market p r ice of capital. Further, the
overall impact on bank equit y of the decline in asset values is proportionate
to the amount of b ank leverage. With highly l everaged banks, a substantial

percentage drop in bank equity ma y arise, leading to a significant disruption
of credit flows. We illustrate this point clearly in section 4.
3 Credit Policie s
Durin g the crisis t h e various c entral ba nks, inclu din g the US. Fed era l Reserv e,
mad e u se of th eir po wers as a lend er o f last re sort t o facilitate c red it flows. T o
justify such actions, the Fed appealed to Section 13.3 of the Federal Reserve
Act, whic h permits it in "unusual end exigen t circumstances" to make loans
to the private sector, s o long as the loans are judged to be of sufficien tly
high grade. The statute mak es clear that in normal times the Fed is not
permitted to tak e on private credit risk. In a crisis, howev er, the Fed has
23
freedom to fulfill its responsibility as lende r of last resort, prov ided that it
does not absorb u ndue risk.
In practice, the Fed employ ed three general t ypes of credit policies. First,
early o n i t expanded d iscount w indow o perations by permitting disco unt
wind ow loans to be collateralized b y high grade private securities and also by
extending the a vailability of the windo w to n on-bank financial institutions.
Second, the Fed len t directly in high grade credit mark ets, funding assets
that in cluded commercial paper, agency d eb t a n d mortgage b ack ed securities.
Third , the Trea sur y, acting in concert with the Fed , injected equ ity in the
banking system along with supplying bank debt guarantees (together with
the Federal Deposit Insurance Corporation).
Thereissomeevidencethatthesetypesofpolicieswereeffective in stabi-
lizing the financial system. The expanded liquidity helped smoothed the flow
of funds bet w een financial institutions, effectively by dampening the turmoil-
induced increases in the spread between the interb ank lending rate (LIBO R )
and the Treasury Bill ra te. The enhanced financial distress following the
Lehm an n failure, howev er, pro ved to be too muc h for the liquid ity facilities
alone to handle. At this point, the Fed set up facilities to lend directly to the
comm ercial paper market and a number of weeks later p hased in program s

to p urchase agency deb t and m ortga ge backed secu rities. Credit spreads in
eac h these mark ets fell.
The equit y i njections also came soon after Lehmann. Though not w ith-
out controversy, the equit y injection s appeared to reduce stress in banking
mar kets. Upon the initial injection of equity in mid-Octo ber 2008, credit
default sw ap rates of th e majo r banks fell d ram atica lly. At the tim e of t h is
writin g, the receiving banks ha ve paid back a considerable portion of the
funds. Further, though r isks remain, t he gov ernm en t appears t o have made
mon ey on man y of these program s.
Inthesub-sectionsbelow,wetakeafir st pass at analyzing ho w these
policies work, using our baseline model.
13
As we sho w ed in the previous
section, within the con text of our model, the financial mark et frictions open
the possibilit y of periods of distress wh ere excess returns on assets are ab-
norm ally high. Because they are balance sheet constrained, private financial
in term edia ries cannot imm ediately arbitrage these returns. On e can view
the poin t of the Fed’s various credit program s as facilitating this arbitrage in
13
For related attempts to model credit policy, see C urdia and Woodford (2009a, 2009b),
Reis (2009), and Sargent and Wallace (1983).
24
times of cr isis. In this regard, each of the various policies w o rks so m ew ha t
differently, as w e discuss belo w .
Before proceeding, we e m p hasize that, con sistent w ith the Federal R eserve
Act, w e have in mind that these in terven tion s be used only during crises and
not durin g normal t imes. Indeed, within the logic o f the model, the net
benefits from credit policy are inc rea sin g in the distortion of cre dit mar kets
that the crisis induces, as measured b y the excess return on capital.
3.1 Lending Facilities ( Direct L ending)

What we mean by direct lending is meant t o bro adly characterize the facilities
the Fed set up for direct acquisition of high qualit y private securities.
Lendin g facilities wo rk as follows: We suppose t h at the central bank has
both an advantage and a disadvantage r elative to private lenders. The ad-
vantageisthatunlikeprivateintermediaries,thecentralbankisnotbalance
sheet constrained (at least in the same way). Private citizens do not have
to worry about the cent ral bank defaulting. The liabilities it issues are gov -
ernment d eb t and it can credibly c om m it to ho norin g this d eb t (aside from
inflation). Thus, in periods of distress where private intermediaries are u n -
able t o obtain additional funds, t he central bank c an obtain funds a nd then
c h ann el them to markets with abnorma l excess returns.
14
In the curren t crisis, the Fed funded the initial expansion of its lending
program s b y issuing g ov ernment debt (th at it borro wed f rom the Tr easur y)
and then later m ade use o f interest bearing reserves. The latter are effectively
go vernmen t debt. It is t rue t hat the interest rate on reserv es fell to zero as
the Federal Funds rate reached its lower bound, giving these reserves the
appearance of money. Ho wever, once the Fed mo ves the Funds rate above
zero it will also raise the interest rate on reserves. In t his r egard, the Fed’s
unconventional policies should be thought of as expanded cen tral interme-
diation as opposed to expanding the money supply. In the case of lending
facilities, a key advan ta ge of the cen t ral bank is that it is not constrained in
its abilit y to funds the sam e way as private interm ed iaries m ay be in time
14
Others have also emphasized how that special nature of government liabilities can give
rise to a productive role for government financial intermediations. See, example, Sargent
and Wallace (1983), Kiyotaki and Moore (2008), Gertler and Karadi (2009), and Shleifer
and Vishny (2010). As originally noted by Wallace (1980), unless there is something
special about government liabilities, the Miller-Modigliani theorem applies to government
finance.

25