Bank Capital and the Macroeconomy:
Policy Considerations
Michael T. Kiley†
Jae W. Sim‡
April 9, 2013
Abstract
We develop a macroeconomic model in which the balance sheet/liquidity condition of financial
institutions plays an important role in the determination of asset prices and economic activity.
The financial intermediaries in our model are required to make investment commitments before a complete resolution of idiosyncratic funding risk that can be addressed only by costly
refinancing, forcing them to behave in a risk-averse manner. The model shows that the balance
sheet condition of intermediaries can drive asset values away from their fundamentals, causing
aggregate investment and output to respond to shocks to intermediaries. We use this model
to evaluate several public policies designed to address balance sheet problems at financial institutions. With regard to short-run policies, we find that capital injections conditioned upon
voluntary recapitalization can be a more effective tool than direct lending/asset purchases.
With regard to long-run policies, we demonstrate that higher capital requirements can have
sizable short-run effects on economic activity, and that a long transition period helps avoid
undesirable side effects. Finally, we show that the mariginal effects of policies can be larger
during "crises" because of the nonlinear interactions between some financial frictions and policy actions.
1
Introduction
Macroeconomic policy actions in recent years have turned to a focus on the strength of the equity
buffer backing banking sector liabilities– with prominent examples including the capital injections
in the United States associated with the Troubled Asset Relief Program (TARP), the "bank stress
tests" in the U.S. and Europe, and the implications of higher capital requirements for banking institutions agreed in the Basel 3 process for credit supply, macroeconomic activity, and the safety of
the banking system. To assess such policy efforts, it is essential to have a model that captures key
We would like to thank seminar participants at the 2011 ASSA meetings, the Board of Governors of the Federal
Reserve System, the Bank of Canada, and the Bank of Japan for comments on an earlier draft (circulated under the title
“The Dynamic Effects of Bank Capital in General Equilibrium”). The views expressed herein are those of the authors,
and do not reflect the views of the Federal Reserve Board or its staff.
† Board of Governors of the Federal Reserve System
‡ Board of Governors of the Federal Reserve System
1
aspects of the dynamic frictions that may cause (at least short-run) deviations from the ModiglianiMiller theorem and hence make the capital structure of the banking sector important for credit
provision. These links are thin to non-existent within the workhorse framework for macroeconomic analysis, although research has begun (for instance, Adrian and Shin (2010), Brunnermeier
and Pedersen (2009), Gertler and Kiyotaki (2010) and He and Krishnamurthy (2012)). Moreover,
banking, finance, and macroeconomics are typically not integrated in the models used in policy
circles (e.g., the discussion in Boivin, Kiley, and Mishkin (2010)).
Our goal in this paper is twofold: First, we develop a dynamic model in which the balance
sheet/liquidity condition of financial institutions plays an important role in the determination of
asset prices and economic activity. Second, using this model, we evaluate the macroeconomic
effects of short-term credit policies aimed at stabilizing the balance sheet/liquidity condition of
troubled financial institutions, and assess the long-term and transitional effects of implementing
higher capital standards. These policies are stylized examples of the types considered in recent
discussions.1
We first describe how the frictions facing households and intermediaries lead shocks to the
intermediary sector to cause fluctuations in investment and output, highlighting three mechanisms. First, we assume, in line with recent research (e.g., Gertler and Kiyotaki (2010) and He
and Krishnamurthy (2012)), that intermediaries are essential for transforming household saving
into investment; while this assumption is strong, we leave relaxation of this assumption to future
work. Second, and more importantly, we emphasize that the mis-match between the timing of
lending commitments and the realization of returns on past lending – that is, the maturity and
liquidity mis-match at the heart of intermediation – causes intermediaries to exhibit caution, or behave in a "risk-averse" manner, in lending. Specifically, the financial intermediaries in our model
are required to make lending commitments before a complete resolution of idiosyncratic funding
risk; moreover, shortfalls in funding relative to lending commitments can be addressed only by
costly external financing. (We emphasize costly external equity financing of the type emphasized
by, for example, Myers and Majluf (1984) and Bolton and Freixas (2000), although other costly
external financing assumptions, including the sale of lending commitments at distressed prices,
1 For a discussion of capital requirements, see BIS (2010a) and BIS (2010b). For a recent summary of the Troubled Asset Relief Program (TARP), which included measures to stabilize the balance sheet position of financial intermediaries,
see Office of the Special Inspector General for the Troubled Asset Relief Program (2009) or CBO (2011).
2
have similar implications.) As a result, intermediaries hold back lending relative to a benchmark
with frictions in external finance and adjust their willingness to lend in response to factors – such
as changes in uncertainty, in the costs of external funds, or in their balance sheet capacity – that
are irrelevant in the absence of financial frictions. Finally, we show how the fluctuations in output
induced by adverse developments within the intermediary sector can be mitigated or amplified
by public policies regarding the capital required to back lending commitments. In particular, we
consider both emergency measures to stabilize the intermediary sector following adverse shocks
– of the type considered in actions such as the TARP and research such as Gertler and Karadi
(2011) – and the effects of regulatory reform in the aftermath of a crisis to raise the required level
of capital as in the Basel 3 process.
We consider two types of stabilization policy: direct lending/asset purchase by a public authority, as in Gertler and Karadi (2011), and a capital injection conditioned on voluntary recapitalization. Our results indicate that the capital-injection policy can be much more powerful than
the direct lending/asset purchase policy in stabilizing output fluctuations. In our baseline simulation, the former turns out to be much more effective than the latter in terms of output stabilization
effects from interventions of the same size. The key mechanism behind this difference is that
an asset purchase policy suffers from a classic case of crowding out: While aggregate investment
is lifted by the increase in government demand, government asset purchases also boosts asset
prices, which causes private investment demand to decline along its downward-sloping demand
curve. Overall, the improvement in liquidity conditions and the business environment associated with direct government lending boosts aggregate demand only moderately. In contrast, the
capital-injection policy increases private demand for capital assets by improving the capital position directly, which boosts the appetite of intermediaries for risky assets. In effect, the capital
injection exploits the willingness of the intermediaries to leverage their balance sheet, thereby
spurring more aggregate investment than government asset purchases.2
Our analysis of higher capital requirements analyzes the transition costs associated with a
substantial increase in the minimum capital ratio for banking institutions, a subject that has been
2 Adrian
and Shin (2010) emphasize the effect of intermediary leverage. He and Krishnamurthy (2008) also suggest
that capital injections are more effective than asset purchases, but their focus is on the asset market recovery. Our framework provides a more comprehensive assessment of impacts of the stabilization policies on employment, investment
and output in a production-based business-cycle framework.
3
the focus of recent debate, as discussed by Admati, DeMarzo, Hellwig, and Pfleiderer (2010) and
Hanson, Kashyap, and Stein (2011), but for which a general-equilibrium quantitative assessment
has been wanting. Our model fills this gap in quantitative assessments. Though we assume that
the capital structure of the financial sector is essentially neutral in the long run (consistent with
the emphasis of Admati, DeMarzo, Hellwig, and Pfleiderer (2010) and Hanson, Kashyap, and
Stein (2011)), shifts in capital requirements can have sizable short-run effects because of the financial frictions facing intermediaries. In the short-run, outside financing is costly because of
(unmodeled) information frictions, whereas internal funds (through retained earnings) are less
costly. Because of this asymmetry in costs, a fast transition to substantially higher capital requirements, which relies to a greater extent on external funds (because retained earnings over a shorter
period are less capable of covering any given increase in required equity) has more adverse effects
on economic activity than a slow transition.
Moreover, we find that the nonlinear interaction between the frictions facing intermediaries
and public policy actions is quantitatively important: Emergency stabilization policies are substantially more effective exactly when they are needed most – in a crisis. Moreover, regulatory
reforms raising capital requirements are much more costly during a financial crisis, and hence
long transition arrangements are especially important for mitigating adverse macroeconomic effects.
We make several contributions relative to the previous literature. As in Gertler and Karadi
(2011), we consider government asset purchases as a stabilization policy, but we also highlight
distinctions between asset purchases and capital injections. As in Gertler and Kiyotaki (2010), we
consider the possible role of subsidies combined with asset purchases, but we provide a quantitative illustration. More importantly, our model is structured quite differently from that of Gertler
and Karadi (2011) or Gertler and Kiyotaki (2010), and highlights how idiosyncratic risk can imply
that a subset of intermediaries become distressed, opening the possibility that targeted interventions work differently than untargeted interventions. In some respects, our framework is more
similar to that of Nuño and Thomas (2012) in emphasizing the potential for time-variation in
idiosyncratic risk within the intermediary sector to have important macroeconomic implications,
although Nuño and Thomas (2012) do not consider the stabilization policies we consider. Finally,
we highlight important differences in the response of financial conditions and economic activity
4
to policy interventions across normal and crisis periods–an emphasis on nonlinearities absent in
related research–and consider issues associated with a transition to a more well-capitalized banking sector that have been of interest to policymakers but relatively unexplored in quantitative
dynamic general equilibrium models.
2
Model
The model consists of a representative household, a continuum of financial intermediaries, a continuum of competitive final-goods producers, a continuum of competitive investment-goods producers, and a government. The model extends that of Kiley and Sim (2011a) through inclusion of
a government sector. The following assumptions are central: First, the complexity of the financial
markets create prohibitively large transaction costs for households. For this reason, households
participate in financial markets only through financial intermediaries, either in the form of deposits, or in the form of ownership of the intermediaries. Second, households value liquidity
services from deposits at financial intermediaries; this assumption is well-founded, as previous
researchers have emphasized how a main purpose of intermediaries is to issue debt with liquidity services such as, but not limited to, deposits (e.g., Gorton and Pennacchi (1990)). As a result,
households accept returns on intermediary deposits below the risk-free rate, creating a strictly positive intermediation margin. Third, the financial intermediaries face a capital (margin) constraint
in their capital structure choice. The constraint creates an environment where financial intermediaries may not be able to fully arbitrage away all profit opportunities because of the constraint on
leverage. Finally, we assume that there is a liquidity/maturity mis-match between intermediaries
assets and liabilities, where lending commitments are made before intermediaries have secured
the funds to back their lending. We start with the financial intermediaries.
2.1
2.1.1
Financial Intermediaries
Return Structure
A financial intermediary i 2 [0, 1] purchases (on behalf of savers) the capital asset Kt+1 (i ) at a
market price Qt ; we refer to such intermediation as "lending". For a streamlined presentation,
5
however, we will omit the index i unless it is strictly required for clarity. The intermediary rents
out this capital to final-goods firms for net rental income defined as
RtK+1 = R̃tK+1 Ut+1
ξ (Ut+1 ) Pt+1
where R̃tK+1 is the nominal rental rate per utilization unit of capital asset (Kt+1 Ut+1 ), Ut+1 is the
utilization rate, ξ (Ut+1 ) is the real cost of utilization and Pt+1 is the price level of the final goods.
The total return from lending is composed of rents/dividends (RtK+1 Kt+1 ) and the capital gains
associated with the changes in the price of capital assets/shares ((1
the depreciation rate of capital.
δ) Qt+1 Kt+1 /Qt ) where δ is
3
To model the balance sheet/liquidity risk that financial intermediaries face, we assume that
the rate of return from lending is subject to a multiplicative idiosyncratic shock such that the total
rate of return can be decomposed into two components, idiosyncratic and aggregate,
RtF+1 (i ) = et+1 (i ) RtF+1
"
RtK+1 + (1 δ) Qt+1
= e t +1 ( i )
Qt
#
(1)
where et+1 is the idiosyncratic component of the return and RtF+1 is the aggregate component.
We assume that the idiosyncratic shock follows a lognormal distribution, log et
N ( 0.5σ2t , σ2t ).
To analyze the effects of changes in uncertainty in financial markets, we assume that the volatility level of the distribution follows an AR(1) process. Despite the fact that this volatility refers
to the uncertainty associated with idiosyncratic risks, changes in volatility have macroeconomic
consequences because they will affect the liquidity risk of intermediaries.
We refer to intermediary activities as "lending", even though our modeling choice implies intermediaries take on underlying risk associated with ownership of the capital asset. Other research, e.g., Gertler and Kiyotaki (2010), takes the same approach.
2.1.2
Capital (Margin) Constraint
To finance the lending described above, the intermediaries mix debt (deposits) and equity. In
doing so, they face a capital (margin) constraint, which requires that every dollar of lending should
3 Equivalently,
the rental income can be thought of as dividends from the final goods firms. In this case, Kt+1 should
be interpreted as the number of shares.
6
be backed by at least mt cents of equity capital. Denoting the amount of borrowed funds by Bt+1 ,
the capital constraint can be stated as
1
Bt+1
Q t K t +1
mt .
(2)
A constraint such as the above can arise in various contexts. In Kiley and Sim (2011a), we show
how such a constraint can be derived from a Value-at-Risk (VaR) constraint such as in Brunnermeier and Pedersen (2009) and Adrian and Shin (2008). In particular, we show that the constraint
can arise as a limit point of VaR constraint, where financial intermediaries are never allowed to
default, i.e., the intermediaries are always required to raise enough amount of equity capital to
stay afloat, a point originally made by Adrian and Shin (2008). Alternatively, Kiley and Sim (2012)
show how a margin constraint, albeit one with additional factors, arises in a model in which
intermediaries may default on a portion of their debt from the discipline imposed by debt holders. Because our goal is to show the implications of such constraint in an environment where
the recapitalization of an intermediary is costly owing to equity market frictions, we avoid the
complications associated with endogenously motivating the capital constraint.
In equilibrium, the capital constraint is always binding for two reasons: First, as mentioned
before, the household is willing to pay a liquidity premium for its deposits since the intermediary deposits create non-pecuniary returns for the household. Second, even without the liquidity
premium, financial intermediaries prefer to issue debt rather than to issue equity owing to the
dilution cost associated with equity issuance, which will be explained shortly. As a consequence,
the financial intermediaries follow a “pecking order” in their capital structure choice.
2.1.3
Modeling Liquidity Risk
The primary function of financial intermediary is the transformation of short-term liquid assets
into long-term illiquid capital assets. Such a transformation exposes the financial intermediaries
to liquidity risk. To model this liquidity risk, we adopt the following timing convention for a given
period of time t:
1. At the beginning of each period, the aggregate component of returns (RtF ) becomes known.
7
2. After observing the aggregate shocks, the intermediary makes lending (Qt Kt+1 ) and borrowing (Bt+1 ) decisions.
3. After the lending/borrowing decisions are made, the level of the idiosyncratic shock (et )
becomes known to the intermediary and dividend payout /equity issuance decisions are
made.
The timing convention implies that the financial intermediaries have to make lending commitments before they know their (random) realization of internal funds. It also implies that the
revenue shock becomes known only after the borrowing markets for intermediaries are closed.
While this precise timing is somewhat arbitrary, it captures important features of reality. In particular, the timing convention represents parsimoniously short-run funding risks. For example,
financial intermediaries always face uncertainty about the balance between their short-run loanable funds and/or the cost of such funds in retail/wholesale borrowing markets and the use of
outstanding loan commitments; alternatively, realized income can fall short of the funding needs
associated with their precommitments due to credit losses or fluctuations in asset values. Under
such conditions and when outside equity is more expensive than borrowing, funding uncertainty
can make the intermediaries adopt a precautionary stance in making investment/deposit decisions
even when all intermediaries are risk-neutral.4
2.1.4
Costly Recapitalization
To capture the role of financial market frictions for the intermediaries, we adopt a costly equity
finance framework. Owing to the information asymmetry between the intermediaries and the
potential owners, equity issuance involves a dilution effect, a phenomenon that a dollar amount
of equity issuance reduces the value of existing shares more than a dollar. We operationalize
this effect by assuming that the actual cash flow related with equity is given by a function ϕ( Dt )
4 A similar timing convention has been used by Gertler and Kiyotaki (2010) in the context of interbank market
borrowing decision of risk neutral banks. Note that interbank borrowing, a possibility from which we abstract, does
not ameliorate the potential funding distortions under realistic assumptions. In particular, borrowing more through the
interbank market to cope with cash flow shortfalls simply worsens any funding shortfall because it increases leverage.
An efficient secondary market for balance sheet assets could help in this situation. However, it is natural to assume
that the same information problem that makes equity finance costly also makes interbank transfer of balance sheet
assets difficult (as was apparent in the financial crisis of 2008, where secondary markets for bank loans became severely
distressed).
8
defined as,
ϕ ( Dt ) = Dt
ϕ̄ minf Dt , 0g =
Dt
if Dt 0
.
(1 ϕ̄) Dt if Dt < 0
(3)
where Dt is cash-flow for equity holders (i.e., dividend payouts or new equity raised from shareholders). When the intermediary pays out a positive amount of dividends, the cash outflow associated with equity is simply given by the dividends, Dt . However when the intermediary issues new equities (Dt < 0), the cash inflow associated with the notional value
(1
ϕ̄) Dt . Following Bolton and Freixas (2000), we call the foregone cash flow
Dt is reduced to
ϕ̄Dt the dilution
cost.5
In each period, financial intermediaries face the following flow of funds constraint,
0 = et RtF Qt 1 Kt + Bt+1
|
{z
}
Cash Inflow
[ R B Bt + Qt Kt+1 + ϕ( Dt )].
| t
{z
}
(4)
Cash Outflow
The cash inflow is composed of revenue from last period’s lending et RtF Qt
1 Kt
and new borrowing
from the household Bt+1 . The cash outflow consists of repayment to the household for last period’s
borrowing RtB Bt , where RtB is the borrowing rate of the intermediary, and new lending Qt Kt+1 . The
last item in (4) is the cash inflow/outflow associated with dividend payments or raising equity,
Dt .6 By rearranging the terms and using the definition of capital, the flow of funds constraint can
be interpreted as the law of motion for equity capital Et , i.e.,
Et = Et
1
+ (et RtF
1) Q t
1 Kt
( RtB
1) Bt
5 In
ϕ ( Dt ) .
(5)
reality, the cost of issuing equity could stem from many sources. For example, outsiders who invest in new
shares of the intermediary may not be able to distinguish a negative income shock from diversion or inefficiency of
management. In such an environment, outsiders need to investigate the balance sheet of the intermediary before they
invest to verify that the intermediary complies with the rule of truthful reporting. Furthermore, as shown by Ross
(1977) and Myers and Majluf (1984), outsiders, not knowing the true investment opportunities of the intermediary,
require initial discounts to protect themselves from “lemons”. This type of friction is evident in market data, where,
for example, equity issuance costs take the form of underwriting fees for investment banks and initial discounts of
seasoned equity offerings (SEOs).
6 An alternative approach considered in Jermann and Quadrini (2009) assumes a quadratic adjustment cost in dividend payouts/equity issuance. Such an assumption is motivated by empirical evidence that dividend payouts are
smooth. In contrast to dividend payouts, equity financing and/or share repurchases are better described as lumpy,
discrete event. In reality, modeling the mix of smooth dividend streams and lumpy equity issuance/share repurchases
jointly would require considering a very complicated corporate financing problem, which lies well outside our interest
in focusing on key factors driving the links between bank capitalization and real economic activity.
9
2.1.5
Value Maximization Problem
An intermediary chooses its lending, borrowing, and dividend policy to maximize shareholder
value. In doing so, the intermediary accounts for the timing convention emphasized above – that
is, that lending and borrowing decisions must be made prior to the realization of its current cash
flow associated with its idiosyncratic return on lending.
To define the optimization problem of an intermediary under the specific timing convention
discussed above, it is useful to introduce an expectation operator that accounts for idiosyncratic
uncertainty, Eit ( )
E( jstA ). The conditioning set of the operator includes all aggregate informa-
tion up to time t (denoted by stA ) and excludes the current realization of the idiosyncratic shock
et .
We can then formally state the value maximization problem of the intermediary as follows.
The intermediary optimizes over Ks+1 , Bs+1 and Ds to maximize its value:
VtB =
∞
max
∑ βs
t
Ks+1 ,Bs+1 ,Ds s=t
Et
Λs i
E [ Ds ]
Ps s
subject to
0
(1
m s ) Q s K s +1
Bs+1
and
0 = Eis fλs [es RsF Qs
1 Ks
+ Bs+1
RsB Bs
Q s K s +1
ϕ( Dt )]g
where Λs is the marginal utility of the representative household, µs and λs are the Lagrangian
multipliers associated with the capital constraint and the flow of funds constraint, respectively.
Note that the intermediary is risk-neutral and discounts the future dividends by the marginal
utility of the representative household, the owner of the institution. Also note that the flow of
funds constraint and its shadow value λs are within the expectation operator Eit ( )–under our
timing assumption, the intermediary has to decide how much to borrow and invest before it comes
to know the value of its idiosyncratic shock es . This implies that the intermediary does not know
its own shadow value of internal funds until the idiosyncratic cash flow shock becomes known
and the intermediary needs to form an expectation based on aggregate conditions. However, this
10
does not imply that the flow of funds constraint holds only in expectation term. As an accounting
identity, it must hold always at the end of the period.
We can summarize the efficiency conditions of the problem as follows,
"
RF
Λ t +1 i
Et +1 [ λ t +1 e t +1 ] t +1
:
= µt (1 mt ) + βEt
Λt
Π t +1
#
"
RB
Λ t +1 i
Et +1 [ λ t +1 ] t +1
: Eit [λt ] = µt + βEt
Λt
Π t +1
Eit [λt ]
K t +1
Bt+1
#
(6)
(7)
Dt : λt = 1/ϕ0 ( Dt )
where Πt+1
(8)
Pt+1 /Pt . On the right side of the efficiency conditions for lending and borrow-
ing, all macroeconomic variables at t + 1 pass through the expectation operator Eit+1 ( ), since
the conditioning set of Eit+1 ( ) includes those variables at time t + 1. In contrast, the efficiency
condition for dividends is not integrated over the idiosyncratic uncertainty. This is because the
dividends/equity financing decisions are made after the realization of the idiosyncratic shock.
To see that the capital constraint binds in the steady state, consider the version of (7) that arises
in the absence of aggregate uncertainty, i.e., when Λt = Λt+1 , Eit [λt ] = Eit+1 [λt+1 ], and Πt+1 = 1,
1
µ
Ei [ λ ]
= βR B .
Since the idiosyncratic uncertainty does not disappear in the steady state, the shadow value of
the flow of funds constraint is still integrated over idiosyncratic uncertainty. Binding capital constraint, i.e., µ > 0 requires βR B < 1. As shown below, this is indeed the case owing to the liquidity
premium households place on deposits.7 By multiplying 1
mt to both sides of (7) and subtracting
the resulting expression from (6), we can merge the two efficiency conditions into
mt Eit [λt ]
= βEt
"
Λ t +1
Λt
Eit+1 [λt+1 et+1 ]
RtF+1
Π t +1
(1
mt )Eit+1 [λt+1 ]
RtB+1
Π t +1
!#
.
(9)
This is the version of the efficiency condition that will be used extensively in our analysis that
follows. To operationalize (9) for a sharper characterization of the equilibrium, we need to show
7 There
are other ways to ensure a binding capital constraint. For example, one can assume that the intermediary is
impatient or subject to a constant death probability. Alternatively, one can introduce preferential tax treatment of debt.
11
how the intermediaries in the model form expectations regarding their liquidity condition, which
is summarized by two measures, Eit [λt ] and Eit [λt et ].
2.1.6
Intermediary Asset Pricing
Our model has a symmetric equilibrium for three reasons: financial intermediaries are risk-neutral;
the first moment of the idiosyncratic shock is time-invariant; and the intermediaries decide how
much to lend and to borrow before the realization of their idiosyncratic shocks. In this symmetric equilibrium, all financial intermediaries choose the same level of lending and borrowing, i.e.,
Kt+1 (i ) = Kt+1 ( j) and Bt+1 (i ) = Bt+1 ( j) for all i and j 2 [0, 1]. This greatly facilitates aggregation. However, dividends/equity issuance decisions are conditioned upon the realization of the
idiosyncratic shock.
After imposing the binding capital constraint and the symmetric equilibrium condition, we
can express the flow of funds constraint as
Dt
ϕ̄ minf Dt , 0g = et RtF Qt
1 Kt
RtB (1
mt
1 ) Qt 1 Kt
m t Q t K t +1 .
At the time of dividend payout/equity issuance decision, all other quantities of the above expression are predetermined. Since the left-hand side is strictly increasing in Dt everywhere, we can
find a unique level of the revenue shock that satisfies the flow of funds constraint with Dt = 0. If
we let Dt = 0 and solve for et , we obtain an equity financing threshold,
e t = (1
If et
mt
1)
1 Q t K t +1
RtB
+ mt F
.
F
Rt
R t Q t 1 Kt
(10)
et , paying out a strictly positive amount of dividends is optimal; in contrast, it is opti-
mal to issue equities (Dt < 0), incurring the dilution cost of ϕ̄, if et < et . This and (8) imply
that the shadow value of internal funds of the intermediaries depends on the realization of the
12
idiosyncratic shock in the following way8 :
λt = 1/ϕ0 ( Dt ) =
1
if et et
.
1/(1 ϕ̄) if et < et
(11)
Two aspects of the value of internal funds are important in guiding intermediaries’ decisions:
Proposition 1 The expected shadow value of internal funds, Eit [λt ] is strictly greater than 1 for all t as
long as ϕ̄ > 0 and σt > 0.
The proof of Proposition 1 is trivial: as long as the probability of costly recapitalization is
greater than zero, i.e., Pr(et < et ) > 0, Eit [λt ] > 1 directly follows from (9). Proposition 1 implies
that the intermediary’s ex ante valuation of a sure dollar is always greater than a dollar as long
as the probability of costly recapitalization is strictly positive. While the realized shadow value
takes only two values: it is either 1 or 1/(1
ϕ̄), the expected shadow value is time-varying as
aggregate conditions change. It is this expected value that matters for the commitment decisions
for lending/borrowing. The more likely is costly equity financing, the higher the expected shadow
value of internal funds.
Proposition 2 1 < Eit [λt et ] < Eit [λt ] for all t as long as ϕ̄ > 0 and σt > 0.
It is not difficult to see the intuition behind proposition 2. Ex post, low values of the idiosyncratic return et are associated with high values of cash flow (λt ) – that is, idiosyncratic returns and
the value of internal cash are negatively correlated, as bad realizations of returns lead to a high
value of cash; this explains the second part of the proposition. Despite the negative covariance,
Eit [λt et ] must exceed 1, as λt is bounded below by 1 (i.e., intermediaries can value cash on hand by
more than 1, but not by less, as in the latter case they return the excess cash to shareholders) and
et integrates to 1 over the support of its distribution. Proposition 2 implies that the intermediary’s
ex ante valuation of its random potential cash-flow is always greater than the mean value of that
cash flow, as low values of realized cash imply a high value of cash.
8 Note that ϕ ( D ) is kinked at e = e , and ϕ0 ( D ) does not exist in a strict sense. However, this is a measure zero
t
t
t
t
event, and hence still integrable. Under our timing assumption, we evaluate λt only within the expectation operator.
In our working papers (Kiley and Sim (2011a) and Kiley and Sim (2011b)), we derive an analytical expression for
Eit [λt ], and show that Eit [λt ] is differentiable, although λt is not. In our symmetric equilibrium, aggregate equilibrium
conditions only depend on Eit [λt ], but not on λt . This allows us to use a perturbation method in our quantitative
analysis of the aggregate economy.
13
(9) implies an intermediary asset pricing formula. Dividing (9) through by mt and rearranging
the terms yields
1 = Et
(
B
Mt,t
+1
"
1
mt
RtF+1
Π t +1
"
#
Eit+1 [λt+1 et+1 ]
Eit+1 [λt+1 ]
(1
RB
m t ) t +1
Π t +1
!#)
(12)
where the intermediary’s pricing kernel is given by
B
H
Mt,t
+1 = Mt,t+1
Eit+1 [λt+1 ]
Eit [λt ]
.
(13)
The above asset pricing formula looks different from a textbook version mainly for two reasons. First, the formula is a levered asset pricing formula. Unlike in the textbook version which
assumes away leverage choice, the returns are levered up to the inverse of capital ratio. To see this
point, assume mt = 1. One can then see that the second term vanish and the formula looks closer
to the conventional one.
Second, the intermediary specific pricing kernel is a filtered version of the representative
household’s pricing kernel, where the filter is the ratio of the shadow value of internal funds
today vs. tomorrow. The filter implies both that developments at intermediaries will affect equilibrium outcomes and potential amplification of developments relative to a model without financial frictions: Suppose that in the beginning of current period, bad news about aggregate returns
arrives. This, holding other things constant, increases the probability of costly recapitalization
(Pr (et < et )) since even a normal range of idiosyncratic return may not be enough to meet the
funding needs associated with today’s lending. If the aggregate shock is strong enough, the ratio
of shadow values tomorrow vs. today substantially declines, making overall required return on
B
capital (1/Mt,t
+1 ) rise, which suppresses today’s lending.
We note that, when ϕ̄ = 0, the asset pricing formula collapses to
1 = Et
(
H
Mt,t
+1
"
1
mt
RtF+1
Π t +1
(1
RB
m t ) t +1
Π t +1
!#)
and idiosyncratic uncertainty plays no role in the determination of asset prices. Any arbitrarily
large amount of uncertainty simply does not matter for real allocations. In this sense, costly equity
finance is the key friction in our framework.
14
The form of the intermediary asset pricing formula is superficially similar to Jermann and
Quadrini (2009), who derive a similar pricing kernel from a reduced-form convex adjustment cost
of dividend; however, our approach derives from a specific set of structural frictions. It is also
superficially similar to the intermediary asset pricing formula of He and Krishnamurthy (2008);
however, they derive their intermediary-specific pricing kernel from the assumption of risk averse
intermediaries. The link to the LAPM (Liquidity-Based Asset Pricing Model) of Holmström and
Tirole (2001) is more direct: In our case, the liquidity premium arises from costly recapitalization
of financial intermediaries, while the premium exists for non-financial corporations with potential
investment opportunity or working capital needs in Holmström and Tirole (2001).
Finally, we introduce the price an intermediary would require to sell/purchase a (hypothetical)
security delivering the cash-flow associated with a loan. Given its pricing kernel, such a security
would be valued by the standard formula,
B
L
1 = Et [ Mt,t
+1 R t ]
(14)
where RtL is the return on the security. In our discussion below, we will refer to the spread observed
in private credit markets relative to a risk-free rate, and such a spread (measured on a one-period
basis and within our model) corresponds to the difference between RtL and the risk-free rate.
2.2
Household
The representative household consumes the final-goods and earns market wages by supplying
labor inputs for the production of final goods. We assume that the household lacks the skill to
directly manage investment projects. For this reason, the household invests its saving through
financial intermediaries. The household can either invest in the shares of the intermediaries or
make deposits to the intermediaries. The household preferences are given by
u(Ct , Ct
1 , Bt+1 /Pt , Ht ) = log(Ct
aCt
ζ
1+ ψ
H
+ θ log
1+ψ t
1)
Z
Bt+1
di .
Pt
(15)
We adopt an internal habit in consumption and a labor disutility separable from the utility of
consumption. To model the value households place on their deposits, we adopt the deposit-in-the
15
utility specification originating from Sidrauski (1967), which captures the non-pecuniary benefits
provided by financial institutions.9
The household problem is straightforward: the household chooses fCt , Ht , Bt+1 , St g to maximize its lifetime utility,
∞
VtH = max ∑ βs t Et u(Cs , Cs
1 , Bs+1 /Ps , Hs )
s=t
subject to a budget constraint,
0 = Wt Ht + RtB Bt
where Bt =
R
Pt Ct
Tt
Z 1
0
PtS St+1 di
Bt+1 +
Z 1
0
[maxf Dt , 0g + PtS
1,t ] St di
(16)
Bt di, Wt is a nominal wage rate, Ht is labor hours, Tt is the lump sum tax, and
St is the number of shares owned by the households outstanding at time t. PtS and PtS
1,t
are
the ex-dividend value of equity at time t and time t value of existing shares outstanding at time
t
1, respectively.10 Under the assumptions given by (15) and (16), the household’s optimality
conditions are given by 11
Ct : Λt =
Bt+1
1
aCt
Ct
1
βEt
a
Ct+1
aCt
"
#
θ/Λt
Λt+1 RtB+1
+ βEt
: 1=
Bt+1 /Pt
Λ t Π t +1
St+1 : 1 = βEt
"
(17)
(18)
#
Λt+1 Dt+1 + PtS+1 + Ξt+1
.
Λt
PtS
(19)
Note that the efficiency condition for holdings of intermediary debt/deposits incorporates the
non-pecuniary benefit–liquidity–of deposits. This creates a liquidity premium, implying a return
on deposits lower than the risk-free rate:
βEt
"
Λ t +1
Λt
R t +1
Π t +1
RtB+1
Π t +1
!#
=
θ/Λt
Bt+1 /Pt
0
9 Gorton
and Pennacchi (1990) provide a review of the liquidity role of intermediary liabilities. Recent applications
also can be found in Van den Heuvel (2008) and Krishnamurthy and Vissing-Jorgensen (2012).
10 In the symmetric equilibrium, PS and PS
t
t 1,t are identical for all financial intermediaries as they do not include
dividend/issuances. However, the distribution of cum-dividend values is non-degenerate.
11 While the derivation of these conditions is straightforward, Kiley and Sim (2011a) provide details.
16
where Rt+1 is a return on a risk-free asset (in zero-net supply) determined by 1 = βEt [(Λt+1 /Λt )
( Rt+1 /Πt+1 )]. In the non-stochastic steady state, we have 1 = βR and
θ/Λ
=1
B/P
βR B ,
which implies that βR B
1 with the inequality strict if θ > 0. As emphasized earlier, this implies
that the capital constraint binds for the intermediaries in the steady state.
Finally, the efficiency condition for shares shows that the asset pricing formula (19) is slightly
modified from the traditional Lucas tree equation due to Ξt+1 . Kiley and Sim (2011b) shows that
Ξt+1 is the financial gains of new shareholders associated with equity financing, and given by
an amount,
ϕ̄qt+1 Eit+1 [ Dt+1 j Dt+1 < 0] where qt+1
Pr( Dt+1 < 0). We have assumed that
equity financing involves a dilution effect that decreases the value of existing shareholders more
than the amount of equity financing. In our framework, the dilution takes the form of initial
discount sales of new shares, and the discounts are financial gains of new shareholder. In general
equilibrium, the gains of new shareholders and the loses of old shareholders offset each other so
that the resource constraint of the economy is not affected by the cost of equity financing. Ξt+1
and (19) ensure general equilibrium consistency.12
2.2.1
Uncertainty, Cost of Capital and Risk Taking
In a textbook for corporate finance, the cost of capital is usually defined as the weighted average
cost of capital, i.e.,
S
E t [ RW
t +1 ] = m t Et [ R t +1 ] + (1
mt ) Et [ RtB+1 ]
(20)
S
where the cost of capital RW
t+1 is a weighted average of return on equity Rt+1 and return on debt
RtB+1 , and obviously, the weight is given by the capital ratio. However, (20) is an average cost
rather than a marginal cost. What is more important for the intermediary’s investment decision
is the latter. The theoretical measure of marginal cost, while not directly observable, can be seen
12 This
is important in that we do not generate any first-order effect from the equity market friction by simply subtracting the cost of equity financing from the resource constraint. The gains of new shareholders ensure that the cost of
equity financing does not appear in the resource constraint. Any effects from the equity market friction come from the
modification of intermediary optimization conditions, not from direct resource costs.
17
from the optimality condition (9). We can rewrite (9) as
Et
|
"
H
i
Mt,t
+1 Et +1 [ λ t +1 e t +1 ]
{z
MB of Investment
RtF+1
Π t +1
#
=
}
mt Eit [λt ] + (1
|
m t )Et
(
H
i
Mt,t
+1 Et +1 [ λ t +1 ]
{z
MC of Investment
)
RtB+1
.
Π t +1
}
(21)
The above equates the marginal benefit (left-hand side) and the marginal cost (right-hand side)
of lending. Evidently it is a weighted average of two components, the one associated with the
marginal cost of raising capital and the one associated with marginal borrowing cost.
In our framework, marginal cost of capital is increasing in the size of the intermediary’s balance sheet, which can be thought of as the degree of risk-taking in our environment. To see this
point, remember that the equity financing threshold is given by
e t = (1
mt
1)
1 Q t K t +1
RtB
+ mt F
.
F
Rt
R t Q t 1 Kt
The threshold is increasing in the size of balance sheet, Qt Kt+1 : the greater the size of the balance
sheet, the more likely an intermediary is to face the recapitalization problem. This causes the
expected shadow value of funding Eit [λt ] and hence the marginal cost of capital to increase. In
short, the cost of capital in our environment is convex. This suggests that in order to have a robust
expansion of balance sheet, there should be either a decline in the borrowing cost RtB+1 or a decline
in uncertainty that lowers the probability of recapitalization such that the downward shift in the
supply of funds can offset the increase in the marginal cost of funding along the supply curve
that is associated with the balance sheet expansion.13 In our quantitative analysis, we show that
the impact of shocks to uncertainty level can be sizable on the funding cost of intermediary and
overall allocation of resources in the macroeconomy.
2.3
Technology
To save space, our description of the rest of the model economy will be brief. While we keep
distinctions between nominal and real variables in our notation (thereby allowing easy integration
of monetary policy questions at a later stage), price adjustment is frictionless in this analysis.
13 One
can formally show that ∂Eit [λt ]/∂σt > 0.
18
2.3.1
Final Goods
A continuum of competitive firms produce final goods using capital and labor in a constant returnto-scale Cobb-Douglas technology. They solve the following static profit maximization problem,
max f Pt Zt (Kt Ut )1
α
Kt Ut ,Ht
( Ht )α
RtK (Kt Ut )g
Wt Ht
where Zt is an aggregate technology shock. Since the scale of the problem is indeterminate, one
could assume a representative firm instead of a continuum.
2.3.2
Fixed Investment
A continuum of competitive firms produce investment goods by combining an input of final goods
and a constant return-to-scale adjustment technology. Following Christiano, Motto, and Rostagno
(2003) and Smets and Wouters (2007), we specify a convex investment adjustment cost and model
the investment problem as follows,
∞
Λs
VtI = max Et ∑ βt s
Ps
Is
s=t
(
Qs Is
Ps
"
χ̄
Is +
2
2
Is
Is
1
1
Is
1
#)
.
Again, the problem is scale-free and can be thought of as the one of a representative firm instead
of a continuum.
2.3.3
Goods Market Clearing Condition
The goods market clearing condition of the model economy is given by
Yt = Ct + It +
χ̄
2
It
It
It
1
1
2
It
1.
(22)
Note the absence of financial flows related with equity issuance costs. As we mentioned earlier,
this is due to our assumption that the dilution cost of equity issuance takes the form of discount
sale, rather than an efficiency loss for the economy.
19
3
Dynamic Responses to Financial Shocks
Before we consider policy-related issues arising from the financial frictions facing intermediaries,
this section illustrates the dynamics of the model using three financial shocks: a balance sheet
shock, a cost-of-equity shock, and an uncertainty shock. A common feature of these shocks, as
we will show below, is that they do not have any implication for real allocations in the absence of
the frictions facing intermediaries described above. We start the discussion with our calibration
strategy.
3.1
Calibration
There are three parameters that govern key aspects of the model’s predictions for the macroeconomic effects of credit policies: the cost of equity issuance ϕ̄, the standard deviation of idiosyncratic return risk σ, and the weight on the deposit in the utility θ. We largely adopt values to
highlight key mechanisms in the model, and emphasize the sensitivity of results to these choices
below. Future work may wish to adopt a more rigorous empirical approach, but we view a discussion of sensitivity as valuable at this stage because of the somewhat stylized nature of our
model; this approach is similar to that of, for example, Gertler and Kiyotaki (2010) and Gertler
and Karadi (2011). As we mentioned earlier, we chose ϕ̄ = 0.30, following Cooley and Quadrini
(2001) to replicate the notion that the opacity of intermediaries’ assets may make external funds
quite costly. Regarding idiosyncratic risk, we set σ = 0.10 (in annual frequency): This value, combined with the cost of external funds, implies a marginal value of a dollar of cash flow, λ, between
1.1 and 1.2 in the steady state. With regard to the weight of deposits in the utility function (θ), we
choose its value to match (roughly) the net interest margin of financial intermediaries, R E
RB .
Saunders and Schumacher (2000) and Demirguc, Laeven, and Levine (2003) provide an international comparison of such margins, which range from a low of 160 bps (Swiss) to a high of 500
bps (Spain and U.S.) on average during the period of 1988-1995. Conditioned upon ϕ̄ = 0.30 and
σ = 0.10, setting θ = 0.07 implies an interest margin near 300 basis points, roughly matching the
interest rate margin in the data. Note that the interest rate margin is a sum of two components,
RF
RB = RF
R+R
R B . With θ = 0.07, about one-third of the margin is explained by a
return premium over risk free rate R F
R and the rest of the margin is explained by the liquidity
20
premium R
R B in our framework.
With regard to other parameters, our implementation assumes that the financial intermediaries
face small costs of dynamically adjusting their balance sheets. In part, this is to replicate the
slow dynamics often found in credit aggregate data. We specify the functional form as quadratic,
i.e., γ̄/2 ( Qt Kt+1 /Qt
1 Kt
1)2 Q t
1 Kt
and set γ̄ = 1. we choose the investment adjustment cost
parameter and the parameter governing habit persistence so as to deliver hump-shaped impulses
response function to typical shocks. For the investment adjustment cost parameter, we set χ̄ =
0.5, a moderate value similar to those reported in macroeconomic analyses (of other issues). We
calibrate the habit persistence parameter as a = 0.75, a value in the typical range.
For the parameters that can be considered traditional, we make standard choices whenever
possible. The risk free rate in the steady state is set at R = 1/β = 1.01 in quarterly frequency.
The depreciation rate δ is set equal to 0.025. We assume a relatively elastic labor supply by setting
the inverse of Frisch elasticity parameter ψ equal to 0.1 and we choose the weight of the labor
disutility as ζ = 1. We set α = 0.60, a fairly standard setting.14
3.2
Role of Balance Sheet Condition: An Illustration
Within our model, any disturbance that alters the balance-sheet (or liquidity) position of intermediaries has important macroeconomic effects. We illustrate this basic point in figure 1, in which
we consider a hypothetical aggregate shock to the balance sheets of financial intermediaries. For
this experiment, we modify the flow of funds constraint as
0 = et RtF Qt
1 Kt
+ Ft + Bt+1
RtB Bt
Q t K t +1
ϕ ( Dt )
where Ft denotes the shock to the balance sheet. The shock is assumed to follow an AR(1) process,
Ft = ρ F Ft
1
+ etF .
14 Kiley
and Sim (2011a) considers a more formal procedure to calibration, matching impulse response functions
following an uncertainty shock. As noted in the text, given the stylized nature of the model and the difficulty in
measuring time-variation in idiosyncratic risk within the intermediary sector, we prefer to highlight the sensitivity of
our results to parameter values rather than to focus on any specific empirical strategy.
21
We consider a relatively transient shock setting ρ F = 0.6 such that the half life of the shock is no
greater than 3 quarters. The size of etF is roughly -20% of the normal level of intermediary equity
capital, as shown in panel (a). For general equilibrium consistency, we assume that the shock is
a lump-sum balance-sheet transfer between the households and the intermediaries. While such
a shock is not "realistic", it will illustrate the key mechanism in the model, and we will consider
shocks to the financial frictions in our model in the next subsection. Finally, note that the shock
is additive to the intermediary profit, and, as such, does not have direct implication for the marginal profitability of intermediary investment. As a result, the shock would not have substantial
real effects on a frictionless economy (i.e., an economy with ϕ̄ = 0). However, under the funding
market friction that we consider, the shock is relevant information for the risk management of the
intermediaries. The shock affects the liquidity condition of the intermediaries, which influences
the marginal valuation of investment opportunity. For a straightforward comparison, figure 1 also
displays the case of the frictionless economy (denoted by black circles) together with the case of
the model economy (blue solid lines). In each case, we summarize credit-spreads through a hypothetical 10-year lending rate relative to the 10-year risk-free rate, as in Gertler and Karadi (2012);
this approach, focusing on long-term yields, facilitates a very rough comparison with experience,
as long-term yields on private credits are observable and spreads on such instruments increased
several hundred basis points during the crisis.15
Consider the frictionless case first. The cash outflow worsens the internal funds position, implying more need for outside equity, reflected in the large rise in the equity issuance cutoff shown
in panel (b). Since the shock does not have implication for the marginal profitability of financial investment, a large number of intermediaries simply cut the dividends (panel (c)). Equity issuance,
shown in panel (d) substantially increases as there is more need for outside funds. Such financial
flows, however, do not have any consequences for real allocations. Since the financial markets are
frictionless, the shadow value of extra cash is always equal to one, not responding to the liquidity
condition as shown in panel (e). As a result, lending spreads (panel (g)) show zero responses.
With no changes in the costs of capital at various levels of the economy, the level of lending is also
unresponsive to the shock (panel (h)), implying no changes in employment, real investment, and
15 As in Gertler and Karadi (2012), this hypothetical spread is computed by applying the expectation hypothesis to
the private lending rate and the risk-free rate to create the hypothetical long=term interest rates.
22
output (panel (i), (k) and (l)).
We now turn to the case with the financial friction. As in the frictionless case, the liquidity condition of the financial intermediaries is dramatically worsened by the shock and the probability of
having to tap the equity market for additional funding rises substantially, indicated by the jump in
the equity issuance threshold et . The responses of dividends and equity issuance are more or less
the same as in the frictionless case. What is different is the large rise in the expected shadow value
of internal funds shown in panel (e). As a consequence, the cost of intermediary capital increases
about 150 basis points in panel (f) and a strong positive spill over effect for general lending terms
ensues as the long-loan spread increases as much as 60 basis points in panel (g). The increase in
the value of internal funds, and accompanying decreased risk appetite, leads the intermediaries to
substantially contract their balance sheet as seen in the decline of lending in panel (h). Investment
and economic activity fall as a result, and there is a strong financial accelerator – as the downturn
in the business cycle worsens the return on intermediary financial investment, further impairing
the liquidity condition of the intermediaries, leading to an even stronger fall in real economic
activity.
3.3
Response to Shifts in Financial Frictions
Given the importance of the balance sheet condition of intermediaries, we can now illustrate how
the model economy responds to changes in key drivers of financial frictions within our model
economy. We consider two examples – an increase in the cost of outside equity, ϕ̄, and an increase
in idiosyncratic risk. Both responses are shown in figure 2. In each case, the parameters follow an
AR(1) process with autoregressive root equal to 0.9.
An increase in the cost of outside equity has predictable consequences, as illustrated by the
solid blue lines in the figure, which reports the consequences of a 10 percent increase in the dilution cost (from 0.30 to 0.33). Specifically, such an increase leads intermediaries to value internal
funds more highly (panel (a)) – as any need to raise equity has a higher cost. In response to the
higher value of internal funds, intermediaries contract their balance sheet (lending) (panel (d)) by
charging a higher spread on loans, with the spread on the hypothetical 10-year loan (panel (b)) increasing about 15 basis points (at an annual rate). Investment and real activity decline as a result,
23
with the former falling near 1-1/2 percent and the latter down near 1/2 percent (panels (e) and
(f)).
Heightened uncertainty – that is, an increase in idiosyncratic risk – has similar consequences,
as illustrated in the black, dashed-dotted lines in the figure (which report the consequences of a
10 percent increase in idiosyncratic volatility). A temporary increase in idiosyncratic risk makes
current balance sheet/lending commitments more risky – that is, more likely to require raising a
substantial amount of outside equity. To be clear, an increase in idiosyncratic risk also raises the
potential for an out-sized positive return and hence a large dividend to shareholders. However,
this positive outcome receives relatively little weight in an intermediary’s valuation of its internal funds, a phenomenon known as “the bad news principle” (Bernanke (1983)). Because of the
greater dispersion in idiosyncratic returns, some intermediaries find themselves with unusually
large amount of cash inflow. However, at the time of investment/borrowing decisions, the increased probability of costly equity financing aggravates intermediaries’ concern for liquidity and
increases the internal valuation of internal funds, as displayed in panel (a). The cost of intermediary capital increases relative to the risk-free rate, which is transmitted to other credit markets
as shown by the increase in the long-loan spread in panel (b). The funding pressure facing the
financial intermediaries should be met by raising internal funds (e.g., cutting back in dividends),
raising outside equity, or by downsizing the balance sheet (e.g., cutting back in lending or sales
of assets). Each of these options is costly to the intermediaries as the outside capital requires dilution costs and deleveraging of the balance sheet implies the loss of the intermediation margin.
As a consequence, the intermediaries in the model economy respond by trying to strike a balance between their options for balance sheet adjustment. As a result, lending (panel (d)) declines,
depressing investment and output (panels (e) and (f)).
3.4
Simulating a Crisis
As in much of the related literature, we are interested in how our model may capture some of
the dynamics associated with a "financial crisis" and on the role of policy actions in mitigating
such dynamics. We will be particularly interested in the degree to which the efficacy of policy
actions differs between normal and crisis periods – that is, the extent to which the nonlinear inter-
24
actions between financial conditions and policy responses is important. To gauge normal times,
we will consider the impact of policy actions around the steady state associated with our baseline
parameter values.
To gauge dynamics in a crisis period, we consider the behavior of the economy following a
large (but transitory) increase in the cost of external funds. We assume that the cost of external
funds ϕ rises to 0.50 (from 0.30). Such a shock to funding leads to a large increase in intermediaries’
valuation of internal funds and in loan spreads, as shown in figure 3, with the spread on a tenyear loan (panel (b)) jumping 300 basis points – consistent with the type of large increase in credit
spreads on long-term credits during strained periods, highlighting how a crisis is a period in
which borrowing markets contract significantly. The contraction in intermediaries’ balance sheets
(panel (d)) implies that economic activity is sharply curtailed, with a large downturn in investment
(about 20 percent) and output (about 5 percent). These "crisis" values are very similar to the crisis
experiments in Gertler and Karadi (2011), Gertler and Karadi (2012), and Gertler and Kiyotaki
(2010).16
4
Policy Experiments
We now turn to the effects of policy actions in normal and crisis periods. We first examine policies
to cushion economic activity. We consider two policy options – direct lending or secondary market
purchases of intermediary assets, as in Gertler and Karadi (2011) and Gertler and Kiyotaki (2010),
and capital injections from the government to distressed banks.
4.1
4.1.1
Stabilization Policies
Direct Lending/Asset Purchase Policy
We first consider a policy under which the government purchases and holds a certain fraction of
capital assets for a certain period of time. The policy is motivated by the fact that a key problem is
16 The similarity is apparent in the declines in investment and output. With regard to financial frictions, Gertler and
Karadi (2012), who as in our analysis emphasize a spread on a hypothetical long-term private lending commitment
because such interest rates are (imperfectly) observable whereas one-quarter expected risky returns are not typically
observable, report a rise in the ten-year lending spread of 300 basis points (on our definition, which is the difference
between the long-term private credit and the risk-free rate; Gertler and Karadi (2012) also report a spread relative to a
risky long-term government bond).
25
that financial intermediaries do not have deep pockets because of their capital constraint. As a result,
at a time when the prices of capital assets are unusually low, the intermediaries cannot sufficiently
exploit opportunities for investment that are profitable absent financial frictions, thus intensifying
the depth and prolonging the duration of downturns (due to an inability to arbitrage inefficient
intermediation wedges, reminiscent of the limits of arbitrage noted by Shleifer and Vishny (1997)).
If a third party which does not suffer from the deep pocket problem, say, the government, can
intervene and purchase some fraction of capital assets, the undesirable downward spiral between
asset prices and aggregate investment can be mitigated.
Let StG,K and StB,K denote the shares of capital assets owned by the government and by the
intermediaries, respectively. Using this notation, the market clearing condition for capital assets
can be expressed as
1 = StG,K + StB,K .
To focus on the effect on intermediaries, we do not consider distortionary taxation or debt financing of the government purchases, and instead assume that the government maintains a balanced
budget and imposes a lump sum tax to meet the balanced budget constraint,
Tt = Qt StG,K
+1 K t +1
RtF StG,K Kt .
(23)
Regarding the government actions, three things are important: First, in our analysis, all capital
assets are homogeneous by construction; as a result, the issue of potential inefficiency of the government in selecting investment projects is not addressed. Second, the policy can generate profits
through the dividends and capital gains channel, and hence the effects on the government budget
cannot be summarized by the initial outlays. Third, the tax policy turns into a transfer policy as
G,K
the government starts implementing an exit strategy that runs down its investment (StG,K
+1 < St ).
We assume the following AR(1) process with a serially correlated shock term for the law of
motion of the government share StG,K ,
G,K
StG,K
+ utG,K , utG,K = ρu utG,K1 + etG,K
+1 = ρ g S t
26
(24)
The process is an AR(2) process with AR(1) and AR(2) coefficients given by ρ g + ρu and
ρ g ρu , re-
spectively. Note that the government asset position is assumed to be a zero in the steady state, and
we are modeling "emergency interventions" that are not anticipated ex ante by intermediaries.17
Finally, we consider asset purchases of two types. In the first, asset purchases are conducted
at market prices Qt , and the government’s return from such asset holdings is the same as that of
intermediaries. In the second, asset purchases are conducted at subsidized prices above the market
price.
4.1.2
Capital Injection Policy
Now consider a policy under which the government purchases the shares of financial intermediaries who also agree to raise some equity in the private market. Importantly, we assume that the
government does not provide equity at the diluted rate provided by the private market – that is, a
unit of government equity injection gives the government a unit on intermediary profits, not the
1/(1
ϕ) > 1 claim associated with a unit of private equity. (We will consider the consequences
of this choice for government finances and compare such actions to subsidized government asset
purchases). This policy is equivalent to the government purchasing a pro rata share of all intermediaries and refunding the equity issuance cost to those intermediaries that raise outside equity
(and not to those who pay dividends).
Let StG (i ) denote the share of an intermediary owned by the government. With this policy, the
market clearing condition of a particular share is given by
1 = StG+1 (i ) + StH+1 (i ),
where StH (i ) is the share owned by the households. Under the assumption that the government
purchases pro rata shares, i.e., StG+1 (i ) = StG+1 , it is straightforward to show that the dilution cost
under the proposed policy is reduced to
Ξt =
ϕ̄(1
StG+1 )qt Eit [ Dt ].
(25)
17 For a consideration of the moral hazard implications of anticipated government interventions, see Gertler, Kiyotaki,
and Queralto (2010).
27
The policy can be seen as equivalent to a subsidy that is proportional to the amount of equity
issuance with the subsidy rate given by the government share.
Again, we assume that the policy is funded by a lump sum tax Tt of households. Assuming a
balanced budget in each period, the government budget constraint is given by
Tt = qt PtS StG+1
qt
i
1 f E t [ Dt ] +
PtS
G
1,t g St .
(26)
To understand the budget constraint, it is useful to remind that qt is the measure of firms that are
issuing new shares at t. Hence the first term on the right side is the money needed to purchase
shares of firms issuing new equities.18 The second term is a product of two terms: the measure of
issuing firms at t
t
1, and time t cum-dividend value of shares owned by the government at time
1.
Finally, the government can earn profits during the implementation of the policy. For a straight-
forward comparison of this policy with direct lending/asset purchase policy, we specify exactly
the same process as in the latter case,
G,S
StG,S
+ utG,S , utG,S = ρu utG,S1 + etG,S .
+1 = ρ g S t
(27)
Again, to ensure that such policy does not affect the long run equilibrium of the economy, we set
the steady state of the government share equal to zero.
4.1.3
Short-Run Stabilization: Asset Purchases vs Capital Injections
We now evaluate the efficacy of the policies introduced above. To compare the two policies in an
almost identical environment, we use the same parameterization, ρ g = 0.85 and ρu = 0.5. With
18 One might wonder why the dilution cost parameter ϕ̄ does not appear in the budget constraint even though the
capital injection is directly linked to the size of dilution effect. The answer is “it does appear” in a hidden form. To see
this point, one needs to understand that the two value measures, PtS and PtS 1,t are linked by an accounting identity: PtS
= PtS 1,t + Xt , where Xt is the value of newly issued shares. Under a perfect capital market condition, Xt is simply given
by qt Eit [ Dt j Dt < 0]. However, under our assumption of frictional capital market, Xt = (1 ϕ̄)qt Eit [ Dt j Dt < 0]. As
we mentioned in the main text, the capital injection policy decreases the size of the dilution effect from ϕ̄ to ϕ̄(1 StG+1 ).
Under this condition, the accounting identity becomes
PtS = PtS
1,t
[1
ϕ̄(1
StG+1 )]qt Eit [ Dt j Dt < 0] = PtS
1,t
(1
ϕ̄)qt Eit [ Dt j Dt < 0]
ϕ̄StG+1 qt Eit [ Dt j Dt < 0].
The last term is the subsidy from the government. Essentially, the government is purchasing shares at an overvalued
price. See Kiley and Sim (2011b) for more detailed derivation.
28
this setting, a one time shock (etG,K or etG,S ) generates a peak in the government’s asset market share
after 3 quarters. Thereafter, the government share undergoes a very slow run-off. We set the sizes
of initial shocks so that the initial outlays equal about 2 percent of output, roughly matching 1 3/4
percent share of GDP that was devoted to bank recapitalization under the Troubled Asset Relief
Program (TARP) (Office of the Special Inspector General for the Troubled Asset Relief Program
(2009)).
Figure 4 presents the economic effects of the two policies around the steady state – that is, in
normal times. The black dashed-dotted line shows the effect of direct lending/asset purchases at
market prices, the black dashed line shows the effects of asset purchases at subsidized prices where
the subsidized prices is 20 percent above the market price, and the blue solid line shows the effect
of capital injections. In panel (a), one can see that the policy experiments are calibrated such
that government outlays relative to aggregate output are roughly the same for asset purchases at
market prices and the capital injections: In these two cases, the government outlays immediately
jumps to 2 percent level in the first period, remain positive for several periods, and then turn
negative, reflecting the earnings on government investments and the runoff of purchases. For
asset purchases at subsidized prices, we assume the same initial government outlay of 2 percent
of GDP, but a different subsequent path of government outlays – one that never falls below zero
– reflecting the lower earnings per dollar of outlay associated with purchasing assets at inflated
prices.
In thinking about government outlays, it is important to emphasize that asset purchases at
market prices and capital injections have a present-discounted value for the government of zero
– that is, future earnings perfectly compensate the government for its outlays. This is not true
for asset purchases at subsidized prices, which involve a substantial transfer from households to
intermediaries. These differences are reflected in the path of government outlays in panel (a),
where one can see such outlays cumulate to zero for asset purchases at market prices and a capital
injection, but cumulate to a positive sum for purchases at subsidized prices.
In panel (f), one can see that the prices of capital assets immediately jump with the policies
in each cases. Given our choice for a relatively small adjustment friction in investment, the magnitude of asset prices responses are not large. Nevertheless, such an increase in the asset prices
improves overall balance sheet conditions of the intermediaries in both cases. One can read this
29
from the drop in the shadow value of internal funds, panel (b).
However, panel (b) reveals a very different picture about the efficacy of the policies in generating desired stabilization effect: The drop in the shadow value, which is the best summary measure
of the liquidity/balance sheet conditions in our framework, is significantly larger for capital injection policy than for asset purchases at market prices, suggesting that the capital injection policy
may be much more powerful than the direct lending/asset purchase policy in handling a liquidity/balance sheet crisis. Subsidized asset purchases are more effective than purchases at market
prices, reflecting the additional cash flow received by intermediaries selling assets.
Overall, the capital injection policy is much more effective relative to its long-run cost. Asset
purchases at market prices have a present-discounted value of zero – future earnings exactly compensate for outlays – but are not very effective. Capital injections also have a present-discounted
value of zero and are effective.. In contrast, subsidized asset purchases – while effective in improving the funding condition of intermediaries – are costly, with outlays substantially exceeding
future earnings on a present-discounted value basis.
Panel (g) and (h) illustrate how the dramatic improvement in intermediary funding condition
under the capital injection (or subsidized asset purchase) policy lead to sizable effects on real
activity: In terms of peak response, the capital injection policy induces 5 to 6 times greater impacts
on aggregate investment and output.
What are the economic drivers of the effectiveness of the alternative policies? Panel (e) provides the answer: In contrast to a capital injection policy, the direct lending/asset purchase policy,
without subsidy, suffers from a classic case of ‘crowding out’, with private lending declining. To
understand this point, it is useful to realize that the two policies act on asset markets differently.
When the direct lending/asset purchase policy is executed, asset prices go up, but the demand of
intermediaries’ for investment/lending projects does not shift, and the private demand for assets
decreases along this stable downward-sloping demand curve, as confirmed by the large decline
in private lending (investment) shown in panel (e).
The capital injection policy works in a different way. It improves the liquidity/balance sheet
conditions of the intermediaries, which increases the risk appetite for capital assets as suggested
by the massive drop in the shadow value in panel (d), making both the prices and the quantities
of asset expand in the same direction. Roughly speaking, the vertical distance between the re30
sponses of private lending in panel (e) explains a large chunk of the difference in the efficacy of
two policies.
More fundamentally, by tying the cash injection to the amount of equity financing, the policy
makes the firms reveal their liquidity conditions and allows the public resources to be directed
to the right place – directly at the location where the problem originates. In contrast, the direct
asset purchase policy strengthens the balance sheets condition of all intermediaries, not only the
cash-strapped institutions, and cannot prevent the ones with large amount of surplus cash flow
from paying out the extra profits as dividends (and perhaps bonuses in reality). Finally, the asset
purchases at subsidized prices is an intermediate case – but one that is relatively ineffective on a
per dollar basis (see panel (a) on the path of outlays), in part because the subsidy is received by all
intermediaries rather than those requiring equity.
At this point, it is important to highlight a few points related to the previous literature. First,
Gertler and Karadi (2011) only consider asset purchases, and hence cannot address the distinctions
we highlight across asset purchases and capital injections. Gertler and Kiyotaki (2010) mention the
notion that subsidies associated with asset purchase or capital injection policies may be important,
but do not provide a quantitative illustration. In addition, Gertler and Kiyotaki (2010) refer to the
distinction between equity injections and asset purchases, but note that such policies are fairly
similar in their framework. This occurs, in part, because they consider an intermediary sector that
is entirely symmetric, whereas we highlight how a subset of intermediaries can become distressed
and how policies, such as equity injections, that focus on these intermediaries, may be particularly
effective. That said, our framework is quite different from that of Gertler and Kiyotaki (2010),
and some of these differences are also important. For example, bankers in Gertler and Kiyotaki
(2010) do not use leverage to enhance lending opportunities from outside government equity;
these bankers only lever their own net worth.
4.1.4
Short-Run Stabilization During A Crisis
We now consider the capital injection and asset purchase policy (without subsidy) during a crisis period. We consider policy responses of the same magnitude as those shown above, but now
simulate these during the crisis shown in the previous section. We emphasize the important non-
31
linearities induced by the financial frictions and leverage constraint. As such, we use a nonlinear
solution algorithm to solve all dynamic paths.19 . This contrasts with, for example, the analysis
of a crisis in Gertler and Kiyotaki (2010) which relies on a (log)linear approximation around their
steady state.
Figures 5 and 6 report the results, with the former illustrating the effect of capital injections
and the latter illustrating that of asset purchases. In each figure, the black, dashed-dotted line
shows the crisis dynamics without policy intervention, and the blue solid line shows the response
with the policy intervention. The differences across policies are striking: The nonlinear aspects of
the model are very important when a crisis is brought about by an increase in the cost of equity. In
particular, capital injection policies are much more effective during a "crisis" than during normal
times, reflecting the high cost of outside equity in the crisis (which, as the reader may recall, is the
shock that precipitates the crisis in our simulation). Indeed, the capital injection nearly eliminates
the crisis (for government outlays, relative to GDP, near those of the TARP in the United States).
In economic terms, this result is not surprising: A capital injection, by relaxing the risk of having
to raising large quantities of outside equity during a period over which such funds are especially
costly, makes intermediaries more willing to lend, thereby boosting investment and output.
Quantitatively, the effect on investment and output is several times larger during a crisis than
during normal times. This adds several points to those found in previous research. First, crisis
policies may be most effective exactly when they are needed. Second, this efficacy depends on
identifying the proper policy to ameliorate the shock: This can be seen be looking at the effectiveness of the asset purchase policy (without subsidy); while the impact of this policy is higher than
during normal times, it is clear once again that capital injections better mitigate the adverse effects
of capital shortfalls. And finally, the substantial change in the responses of economic variables
across the normal period and crisis period simulations emphasizes how the nonlinear effects of
financial frictions can be important – raising an important challenge for future research, as fullblown stochastic simulation of models with the range of nonlinear interactions we present is a
substantial computational challenge.
Finally, the asset purchase is relatively ineffective, because in does not address the friction
19 See Boucekkine, Germain, and Licandro (1997) and Adjemian, Bastani, Juillard, Mihoubi, Perendia, Ratto, and
Villemot (2011) for a description of the algorithm.
32
(costly equity) precipitating the crisis, and the size of the crisis is essentially the same with or
without government intervention (figure 6).
4.2
Transitional Dynamics to Higher Levels of Capitalization
Recent years have seen increased attention to the possible effects of a transition to a more wellcapitalized banking sector from academics (Admati, DeMarzo, Hellwig, and Pfleiderer (2010) and
Hanson, Kashyap, and Stein (2011)) and policymakers (BIS (2010b) and BIS (2010a)). The current
policy proposal from the Basel 3 process envisions a roughly 5 percentage point increase in the
required ratio of common equity to risk-weighted assets (from 2 percent to 7 percent) or in the
ratio of tier 1 capital to risk-weighted assets (from 4 to 8 percent). In the data, overall capital ratios
have substantially exceeded these minima, both because regulators have defined well capitalized
as some notable margin above the minimum and because market pressures have led financial
institutions to maintain capital buffers. Consistent with various policy analyses, we assume that
the increase in the regulatory minimum is passed through to overall capital ratios and consider an
increase in the overall ratio of capital to assets from 10 percent to 15 percent.
In our model, the level of the capital requirement is essentially neutral with respect to real economic variables: A higher capital requirement implies that intermediaries must cut their reliance
on debt/deposits; to do so, intermediaries offer a lower rate of return on deposits and this decline
yields no change in the required return to capital; hence the levels of lending, investment, output,
hours, and consumption, are largely unaffected. Kiley and Sim (2011a) and Kiley and Sim (2011b)
present details on this issue. As a result, the costs, in terms of output, of a change in capital requirements only operates along the transition, as output is unchanged in the long-run. This effect
is reminiscent (albeit different) of the Modigliani-Miller effect emphasized in some discussions of
capital policy.20 We emphasize that we could include other reasons why debt/deposits are attractive, such as a tax preference, which would imply that there were steady-state effects on economic
activity, but our analysis of transition issues would not be greatly affected.
We design two transition arrangements to compare two cases, fast vs slow transitions: one in
20 While the long-run neutrality for the return to lending, output, etc., with respect to the amount of equity backing
bank liabilities is reminiscent of the Modigliani-Miller effect emphasized in some discussions, the mechanism in our
model is different–operating through the downward-sloping demand for deposits implied by our deposit-in-the-utility
framework; we simply highlight this similarity to emphasize that we do not focus on long-run effects of intermediary
capital.
33
which the capital ratio is raised by 5 percentage points over a year and the other in which the
capital ratio is raised by the same amount, but over about 10 years. To achieve the transitional
paths for the minimum capital ratio, we assume the following data generating process for the
minimum capital ratio,
log mt = log mt
δt = ρvt
1
1
+ δt ,
+ ut .
By setting an appropriate value ρ, one can control how fast the capital ratio reaches a new long
run value. In the case of fast transition, we set ρ = 0.25 while we ρ = 0.90 for the case of slow
transition.
Figure 7 displays the two transitional paths for selected endogenous variables under the baseline calibration, starting from the steady state. Panel (a) shows the two transition arrangements
for the permanent increase in regulatory capital ratio. In both cases, financial intermediaries face
capital shortfalls, creating funding pressure, which leads to higher value of internal funds at intermediaries as shown in panel (b). However, the slower transition is associated with a disproportionately milder rise in the value of internal funds. As a consequence, the spillover effect on
the general lending terms in other financial markets, shown in panel (c), is much more mitigated:
while the fast transition results in a jump of 100 basis points in the long-loan spread, this spread
rises only a touch in the case of a slow transition.
In panel (d), one can see why the slower transition is associated with smaller financial costs.
The picture displays how much of the required increase in capital at each point in time is obtained by the costly equity issuance. In the faster transition case, the intermediaries have to tap
equity market more intensively as the funding needs far outstrip the available cash flows. Panel
(f) highlights the same point from a different angle: the faster transition is associated with much
more aggressive contraction in lending. As both equity finance and decreasing lending are costly
to the banks, intermediaries balance the two margins. Finally, as predicted by the effects on the
credit spreads and lending, panel (e), (g) and (h) show that the faster implementation takes a much
greater toll on economic activity: the declines in hours, lending, investment and output are about
2 to 3 times greater for the case of a faster transition.
34
Another interesting question regards the degree to which the transition costs would be higher
during a stressful period. For example, the impetus for regulatory reform was the financial crisis. While conditions have improved considerably in the United States, the banking sector and
economic activity are under more severe strains in some other countries as of this draft (in early
2013). To consider the potential effects outside the steady state, we consider the same transition
arrangements during a crisis period as defined above.
Figure 8 presents results for the marginal effect of the transition. Specifically, we show changes
from the crisis paths induced by the transition policies: As a result, the results are comparable
to those in figure 7 analyzing a transition in "normal" times; the total paths for each variable,
including the marginal effect of the transition and the direct effect of the crisis, is given by the
sum of the paths in figures 8 and 3. As with the stabilization policies emphasized above, there are
important nonlinear interactions between a transition to higher capital requirements and a period
of elevated costs of outside equity. As a result, the transition costs are much higher during a crisis
period, and the benefit of a slower transition, as proposed for the Basel 3 process, are considerable
if the transition begins during a period of financial strains.
With regard to these results, we emphasize that little research has considered these questions.
BIS (2010b) and BIS (2010a) largely use reduced-form or large-scale econometric models, often
without a banking sector, to consider these issues.
5
Conclusion
In this research, we consider a tractable macroeconomic model in which real investment is intermediated through institutions that commit financial resources amid idiosyncratic funding risk under a binding capital constraint. We show that the financial frictions facing intermediaries imply
that shocks affecting the balance sheet of intermediaries have important effects on real economic
activity.
We then consider credit policies designed to address liquidity/balance sheet problems at intermediaries and show that a capital injection policy conditioned on voluntary recapitalization is
relatively efficient because it does not suffer from a “crowding out” effect on private investment.
In contrast, asset purchases are relatively ineffective unless they involve a substantial subsidy.
35
Such subsidies are much more costly, within our model, to the government and households than
capital injections.
With regard to long-run policies, we demonstrate that a transition to higher capital requirements can have sizable short-run effects on economic activity if such a transition involves raising
substantial and costly outside equity, as under a rapid transition arrangement.
Finally, we illustrate how the effects of stabilization or transition policies are larger during
a "crisis" in which outside funds become costly. Such nonlinearities are important to highlight
for two reasons. First, in economic terms, these nonlinear relationships imply that stabilization
policies may be most effective when needed – during a crisis – and that policymakers should
consider how the effects of regulatory reform may differ if adopted during a period of financial
stress. From a more purely research perspective, the nonlinearities we highlight show the need
for improved computational strategies to simulate model economies with financial frictions in a
stochastic environment.
Looking forward, our analysis highlights several areas for future research. First, we considered a simple leverage constraint on intermediaries, but have developed similar results in a model
where a leverage constraint arises endogenously as a reflection of default risk and the costs of outside equity. This type of framework can consider macroprudential policy rules (as in Kiley and
Sim (2012)), rather than simple policy interventions as considered herein. Our work and that of
Nuño and Thomas (2012) highlight the potential importance of changes in risk facing intermediaries, and more empirical work to guide such modeling is desirable. Finally, we emphasize capital
regulation, but it is also important for macroeconomic modeling to begin to consider quantitative
models in which liquidity risks may play a role.
References
A DJEMIAN , S., H. B ASTANI , M. J UILLARD , F. M IHOUBI , G. P ERENDIA , M. R ATTO , AND S. V ILLE MOT (2011): “Dynare: Reference Manual, Version 4,” Dynare Working Papers 1, CEPREMAP.
A DMATI , A. R., P. M. D E M ARZO , M. F. H ELLWIG , AND P. P FLEIDERER (2010): “Fallacies, Irrelevant Facts, and Myths in the Discussion of Capital Regulation: Why Bank Equity Is Not
Expensive,” Research Papers 2065, Stanford University, Graduate School of Business.
36
A DRIAN , T., AND H. S. S HIN (2008): “Financial intermediary leverage and value at risk,” Staff
Reports 338, Federal Reserve Bank of New York.
(2010): “Financial Intermediaries and Monetary Economics,” vol. 3 of Handbook of Monetary
Economics, pp. 601 – 650. Elsevier.
B ERNANKE , B. S. (1983): “Irreversibility, Uncertainty, and Cyclical Investment,” The Quarterly
Journal of Economics, 98(1), pp. 85–106.
BIS (2010a): “Assessing the macroeconomic impact of the transition to stronger capital and liquidity requirements,” Interim report of the macroeconomic assessment group, Basel Committee
on Banking Supervision, Basel, Switzerland.
(2010b): “An assessment of the long-term economic impact of stronger capital and liquidity requirements,” Discussion paper, Basel Committee on Banking Supervision, Basel, Switzerland.
B OIVIN , J., M. T. K ILEY, AND F. S. M ISHKIN (2010): “How Has the Monetary Transmission Mechanism Evolved Over Time?,” vol. 3 of Handbook of Monetary Economics, pp. 369 – 422. Elsevier.
B OLTON , P., AND X. F REIXAS (2000): “Equity, Bonds, and Bank Debt: Capital Structure and Financial Market Equilibrium Under Assymetric Information,” The Journal of Political Economy, 108(2),
pp. 324–351.
B OUCEKKINE , R., M. G ERMAIN , AND O. L ICANDRO (1997): “Replacement Echoes in the Vintage
Capital Growth Model,” Journal of Economic Theory, 74(2), 333–348.
B RUNNERMEIER , M. K., AND L. H. P EDERSEN (2009): “Market Liquidity and Funding Liquidity,”
Review of Financial Studies, 22(6), 2201–2238.
CBO (2011): “Report on the Troubled Asset Relief Program,” Pub. No. 4253, Congressional Budget
Office.
C HRISTIANO , L., R. M OTTO , AND M. R OSTAGNO (2003): “The Great Depression and the
Friedman-Schwartz Hypothesis,” Journal of Money, Credit and Banking, 35(6), 1119–1197.
C OOLEY, T. F., AND V. Q UADRINI (2001): “Financial Markets and Firm Dynamics,” The American
Economic Review, 91(5), pp. 1286–1310.
D EMIRGUC , A., L. L AEVEN , AND R. L EVINE (2003): “The impact of bank regulations, concentration, and institutions on bank margins,” Policy Research Working Paper Series 3030, The World
Bank.
G ERTLER , M., AND P. K ARADI (2011): “A model of unconventional monetary policy,” Journal of
Monetary Economics, 58(1), 17 – 34, Carnegie-Rochester Conference Series on Public Policy: The
Future of Central Banking April 16-17, 2010.
(2012): “QE 1 vs. 2 vs. 3... A Framework for Analyzing Large Scale Asset Purchases as a
Monetary Policy Tool,” Working papers.
G ERTLER , M., AND N. K IYOTAKI (2010): “Financial Intermediation and Credit Policy in Business
Cycle Analysis,” vol. 3 of Handbook of Monetary Economics, pp. 547 – 599. Elsevier.
37
G ERTLER , M., N. K IYOTAKI , AND A. Q UERALTO (2010): “Financial Crises, Bank Risk Exposure
and Government Financial Policy,” mimeo.
G ORTON , G., AND G. P ENNACCHI (1990): “Financial Intermediaries and Liquidity Creation,” Journal of Finance, 45(1), 49–71.
H ANSON , S. G., A. K. K ASHYAP, AND J. C. S TEIN (2011): “A Macroprudential Approach to Financial Regulation,” Journal of Economic Perspectives, 25(1), 3–28.
H E , Z., AND A. K RISHNAMURTHY (2008): “Intermediary Asset Pricing,” NBER Working Papers
14517, National Bureau of Economic Research, Inc.
(2012): “A macroeconomic framework for quantifying systemic risk,” Working Paper Research 233, National Bank of Belgium.
H OLMSTRÖM , B., AND J. T IROLE (2001): “LAPM: A Liquidity-Based Asset Pricing Model,” The
Journal of Finance, 56(5), pp. 1837–1867.
J ERMANN , U., AND V. Q UADRINI (2009): “Macroeconomic Effects of Financial Shocks,” NBER
Working Papers 15338, National Bureau of Economic Research, Inc.
K ILEY, M. T., AND J. W. S IM (2011a): “Financial capital and the macroeconomy: a quantitative
framework,” Finance and Economics Discussion Series 2011-27, Board of Governors of the Federal Reserve System (U.S.).
(2011b): “Financial capital and the macroeconomy: policy considerations,” Finance and
Economics Discussion Series 2011-28, Board of Governors of the Federal Reserve System (U.S.).
(2012): “Intermediary Leverage, Macroeconomic Dynamics and Macroprudential Policy,”
mimeo, Board of Governors of the Federal Reserve System.
K RISHNAMURTHY, A., AND A. V ISSING -J ORGENSEN (2012): “The Aggregate Demand for Treasury
Debt,” Journal of Political Economy, 120(2), 233 – 267.
M YERS , S. C., AND N. S. M AJLUF (1984): “Corporate financing and investment decisions when
firms have information that investors do not have,” Journal of Financial Economics, 13(2), 187 –
221.
N UÑO , G., AND C. T HOMAS (2012): “Bank leverage cycles,” Banco de EspaÃśa Working Papers
1222, Banco de EspaÃśa.
S PECIAL I NSPECTOR G ENERAL FOR THE T ROUBLED A SSET R ELIEF P ROGRAM , O. (2009):
“Emergency Capital Injections Provided To Support the Viability of Bank of America, Other
Major Banks, and the U.S. Financial System,” Discussion Paper SIGTARP-10-001, Office of the
Special Inspector General for the Troubled Asset Relief Program.
OF THE
R OSS , S. A. (1977): “The Determination of Financial Structure: The Incentive-Signalling Approach,” The Bell Journal of Economics, 8(1), pp. 23–40.
S AUNDERS , A., AND L. S CHUMACHER (2000): “The determinants of bank interest rate margins:
an international study,” Journal of International Money and Finance, 19(6), 813 – 832.
S HLEIFER , A.,
pp. 35–55.
AND
R. W. V ISHNY (1997): “The Limits of Arbitrage,” The Journal of Finance, 52(1),
38
S IDRAUSKI , M. (1967): “Inflation and Economic Growth,” The Journal of Political Economy, 75(6),
796–810.
S METS , F., AND R. W OUTERS (2007): “Shocks and Frictions in US Business Cycles: A Bayesian
DSGE Approach,” The American Economic Review, 97(3), 586–606.
VAN DEN H EUVEL , S. J. (2008): “The welfare cost of bank capital requirements,” Journal of Monetary Economics, 55(2), 298 – 320.
39
Figure 1: Impact of Balance Sheet Shock
(a) BS shock, % of BS
(b) equity cutof f , %
(c) div idends pay outs, %
5
0
-5
-10
-15
-20
0
10
2
0
1
-20
0
-40
20
0
(d) equity issuance, %
10
20
0
(e) shadow v alue, %
8
60
6
40
4
20
2
50
0
0
0
-20
-2
10
20
150
100
0
(g) Long-loan spread, bps (ar)
80
0.1
60
20
0
10
20
10
20
(i) labor hours, %
0.1
0
-0.1
-0.2
-0.2
0
0
(h) lending, %
-0.1
20
-20
10
0
40
20
(f ) cost of capital, bps
80
0
10
-0.3
0
(j) consumption, %
10
20
-0.4
0
(k) inv estment, %
10
20
(l) output, %
0.1
0.1
0.05
0
0
0
-0.5
-0.1
-0.05
-0.2
-1
-0.1
0
10
20
0
10
20
-0.3
0
10
20
NOTE: Blue, solid lines are the case with financial frictions, and black circles are the frictionless case.
The shock to the balance sheet generates an immediate loss of 20 percent of initial bank capital.
40
Figure 2: Impacts of Dilution Cost and Volatility Shocks
(a) v alue of internal f unds
(b) Long-loan spread, bps (ar)
20
1.22
15
1.21
10
1.2
5
1.19
0
1.18
0
10
20
30
-5
40
0
10
(c) labor hours, %
0.2
0
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
0
10
20
30
30
40
30
40
30
40
(d) lending, %
0.2
-0.8
20
-0.8
40
0
10
(e) inv estment, %
20
(f ) output, %
1
0.1
0
0
-0.1
-1
-0.2
-0.3
-2
-0.4
-0.5
-3
0
10
20
30
40
0
10
20
NOTE: Blue, solid lines are for the dilution cost shock and black, dashed-dotted lines
are for the volatility shock. Both shocks are 10 percent increase from their normal levels.
41
Figure 3: Simulation of Crisis
(a) v alue of internal f unds
(b) Long-loan spread, bps (ar)
1.6
300
1.5
200
1.4
1.3
100
1.2
0
1.1
1
0
10
20
30
40
-100
0
10
(c) labor hours, %
2
0
0
-2
-2
-4
-4
0
10
20
30
-6
40
0
10
(e) inv estment, %
1
0
0
-5
-1
-10
-2
-15
-3
-20
-4
0
10
20
30
40
20
30
40
30
40
(f ) output, %
5
-25
30
(d) lending, %
2
-6
20
-5
40
0
10
20
NOTE: The crisis is generated by elevating the level of dilution cost from its normal
level of 0.30 to 0.50.
42
Figure 4: Unconventional Policies: Asset Purchases vs Capital Injection
(a) Gov ernment outlay s, % of GDP
(b) v alue of internal f unds
2
1.2
1
1.19
0
1.18
-1
0
10
20
30
1.17
0
40
(c) Long-loan spreads, bps (ar)
2
0
0
-5
-2
-10
-4
0
10
20
30
20
30
40
(d) equity issuance, %
5
-15
10
-6
40
0
(e) lending, %
10
20
30
40
(f ) asset prices, %
0.4
1
0.2
0.5
0
0
-0.2
-0.4
0
10
20
30
-0.5
40
0
10
(g) inv estment, %
20
30
40
30
40
(h) output, %
2
0.6
0.4
1
0.2
0
-1
0
0
10
20
30
-0.2
40
0
10
20
NOTE: Blue, solid lines are the case of capital injection policy, the black, dashed-dotted
lines are the case of asset-purchase policy at market prices, and the dashed-black lines
are the case of the asset purchase policy at subsidized prices. See the main text of the
designs of the policies.
43
Figure 5: Capital Injections in a Crisis
(a) Gov ernment outlay s, % of GDP
(b) v alue of internal f unds
3
1.6
2
1.4
1
1.2
0
-1
0
10
20
30
1
40
0
(c) Long-loan spreads, bps (ar)
150
200
100
100
50
0
0
0
10
20
30
20
30
40
(d) equity issuance, %
300
-100
10
-50
40
0
(e) lending, %
10
20
30
40
(f ) asset prices, %
2
5
0
0
-2
-5
-4
-6
0
10
20
30
-10
40
0
10
(g) inv estment, %
20
30
40
30
40
(h) output, %
10
2
0
0
-2
-10
-20
-4
0
10
20
30
-6
40
0
10
20
NOTE: Blue, solid lines are the case with the capital injection policy, and black, dasheddotted lines are the case without the policy. See the main text for the design of the policy.
44
Figure 6: Asset Purchases in a Crisis
(a) Gov ernment outlay s, % of GDP
(b) v alue of internal f unds
2
1.6
1
1.4
0
1.2
-1
0
10
20
30
1
40
0
(c) Long-loan spreads, bps (ar)
150
200
100
100
50
0
0
0
10
20
30
20
30
40
(d) equity issuance, %
300
-100
10
-50
40
0
(e) lending, %
10
20
30
40
(f ) asset prices, %
5
0
0
-2
-5
-4
0
10
20
30
-10
40
0
10
(g) inv estment, %
20
30
40
15
20
(h) output, %
5
0
0
-5
-2
-10
-15
-20
-4
0
10
20
30
40
0
5
10
NOTE: Blue, solid lines are the case with the asset purchase policy, and black, dasheddotted lines are the case without the policy. See the main text for the design of the policy.
45
Figure 7: Transition to a Higher Capital Requirement
(a) capital ratio, %
(b) v alue of internal f unds
16
1.35
1.3
14
1.25
12
10
1.2
0
10
20
30
1.15
0
40
(c) Long-loan spreads, bps (ar)
100
50
50
0
0
10
20
30
20
30
40
(d) recapitalization share, %
100
0
10
40
0
10
(e) labor hours, %
20
30
40
30
40
30
40
(f ) lending, %
0.2
0.2
0
0
-0.2
-0.2
-0.4
-0.4
-0.6
0
10
20
30
-0.8
40
0
10
(g) inv estment, %
20
(h) output, %
0.5
0
0
-0.5
-0.2
-1
-1.5
-2
-0.4
0
10
20
30
40
0
10
20
NOTE: Blue, solid lines are the case of fast transition arrangement, and black, dasheddotted lines are the case of gradual transition arrangement. See the main text for the
details of implementation.
46
Figure 8: Transition to a Higher Capital Requirement in a Crisis
(a) capital ratio, %
(b) v alue of internal f unds
16
1.5
1.4
14
1.3
12
10
1.2
0
10
20
30
1.1
0
40
(c) Long-loan spreads, bps (ar)
200
150
150
100
100
50
50
0
0
0
10
20
30
20
30
40
(d) recapitalization share, %
200
-50
10
-50
40
0
10
(e) labor hours, %
20
30
40
30
40
30
40
(f ) lending, %
0.5
0
0
-0.5
-0.5
-1
-1
-1.5
-2
0
10
20
30
-1.5
40
0
10
(g) inv estment, %
20
(h) output, %
2
0
0
-2
-0.5
-4
-1
-6
0
10
20
30
-1.5
40
0
10
20
NOTE: Blue, solid lines are the case of fast transition arrangement, and black, dasheddotted lines are the case of gradual transition arrangement. See the main text for the
details of implementation.
47