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Credit Lines and Capital Adequacy∗

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					                Credit Lines and Capital Adequacy
                                      Elizabeth Footey
                                     Job Market Paper
                                     29 November 2010


                                             Abstract
          I show how capital regulations, by imposing a low or zero cost on undrawn
      credit lines, can lead to ex post misallocation of credit across borrowers following
      a market shock. This e¤ect is in addition to the liquidity impact of credit line
      drawdowns highlighted by existing literature. In a theoretical model, I draw im-
      plications for both monetary policy and capital regulations. I also show suggestive
      empirical evidence consistent with this mechanism. A credit line, as a commitment
      to lend from a bank, provides a signal of …rm quality to the market, making it
      easier for the …rm to obtain a market loan. Credit lines therefore generate surplus
      when undrawn; yet, under Basel I and II, they face low or zero capital require-
      ments whilst they remain undrawn. A bank has an incentive to build up exposure
      to credit lines if it expects few drawdowns. However, this will constrain its balance
      sheet when credit market turmoil causes …rms to draw heavily on existing lines.
      Given the extra capital requirement it has to face to meet drawdowns, the bank
      will ration lending to other borrowers. I explore why a choice made optimally, ex
      ante, by the bank can lead to such ex post misallocation of credit across borrowers.
      I show that a low interest rate in the good state will worsen misallocation in the
      bad state; if agents anticipate interest rates will be low in good times, banks will
      increase their exposure ex ante in order to bene…t from the surplus generated in
      good times. Furthermore, if a su¢ ciently high capital charge is imposed on un-
      drawn lines, banks will reduce exposure, leading to a reduction in misallocation
      ex post. Finally, I present implications for countercyclical capital regulation; a
      lower capital requirement in the bad state will serve to reduce misallocation in the
      bad state.

      I am grateful to my supervisor Amil Dasgupta for numerous discussions and advice regarding this
paper. I thank Daniel Ferreira for advice on the empirical section. I also thank Ulf Axelson, Mike
Burkhart, Maria Cecilia Bustamente, Mikhail Chernov, Alex Edmans, Sujit Kapadia, Andrew Mell,
Philippe Mueller, Francesco Nava and seminar participants at LSE for helpful comments.
    y
      Department of Economics and Financial Markets Group, London School of Economics and Po-
litical Science, Houghton Street, London, WC2A 2AE, UK. Email: e.e.foote@lse.ac.uk. URL:
http://personal.lse.ac.uk/foote/creditlines.pdf
1       Introduction
1.1      Overview
This paper focuses on why banks build up exposure to credit lines and how this can
a¤ect new credit supply following a market shock. Traditional models of bank lending
focus on standard, term loans, in which borrowers take the funds with certainty at the
beginning of the contract. In reality, a signi…cant proportion of bank lending operates
through credit lines. In these contracts, banks commit to lend, but funds are only ‘ drawn
                                             1
down’if required by the …rm at a later date. The bank faces uncertainty about whether
or not it will be called upon to provide funds.
    Recent evidence suggests credit lines play a crucial role in a¤ecting the supply of new
credit, particularly in times of market turmoil. At these times, …rms that are unable
to obtain market …nancing draw down signi…cantly on their credit lines; Ivashina and
Scharfstein (2009) document this e¤ect following the Lehman collapse, whilst the Bank
of England documents that corporate drawdowns increased in the last quarter of 2007
(Bank of England (2008a)). Ivashina and Scharfstein (2009) follow earlier papers to
argue that credit line drawdowns are like a liquidity shock for the bank.2 Banks with
higher drawdowns face a greater drain on liquidity, thus constraining their ability to
supply newly originated credit. They provide evidence that banks with higher credit
line exposure (more undrawn lines) had lower growth of new credit during the crisis.
    However, I argue there is an additional channel through which credit line exposure
a¤ects future bank credit origination. This operates through the role of regulatory
                                                    o¤
capital requirements. Undrawn credit lines are ‘ balance sheet’ and so do not face
a full capital charge commensurate with equivalent loans that are ‘      on-balance sheet’ .
However, once the line is drawn down, it becomes a balance sheet item and faces a
full capital charge. A drawdown shock is therefore like a shock to regulatory capital
requirements. The implications of credit lines for the regulatory position of a bank are
indeed signi…cant, as the IMF points out in 2008:

        “Using the standards of Basel I, Fitch Ratings (2007) estimated that, under
        a worst-case scenario, if liquidity lines were to be fully drawn down, declines
        in the Tier 1 capital ratio of European banks would peak at 50 percent and
        for U.S. banks at almost 29 percent” (International Monetary Fund (2008)
        p.77).3
    1
     Credit lines can represent various degrees of commitment. Some are simply intentions to lend which
do not bind the bank, whilst others are irrevocable. In many cases, lines may be contingent upon the
borrower meeting certain conditions at the time of drawdown.
   2
     Earlier papers highlighting this issue include Gatev et al. (2009), Gatev and Strahan (2006) and
Kashyap et al. (2002).
   3
     In this paper, I focus on irrevocable commitments. Under Basel I, irrevocable commitments of
maturity less than 1 year face no capital charge. Under Basel II, this has been altered: they have a
credit conversion factor (CCF) of 20% and principal risk factor (PRF) of 100%. Whilst this increases
the capital charge, it still means the o¤ balance sheet item faces a lower capital charge than if it were
a drawn loan. Moreover, Basel II was not fully implemented by 2007.
  Importantly, for all revocable commitments, both the CCF and PRF under Basel II remain 0%.



                                                   1
    A bank which suddenly faces a large amount of drawdowns may …nd it approaches
its regulatory capital constraint. If it is unable to readily raise new capital, it will have
to cut back on the amount of newly originated loans it plans to make. This will result
in a suboptimal allocation of credit; i.e., the marginal return on projects funded via
drawdowns will be lower than the marginal return on newly originated loans.
    Why, ex ante, would a bank set its optimal exposure so high that this may cause
                                                                               t
a suboptimal allocation of credit ex post, in the bad state? Why doesn’ it just o¤er
standard bank loans, thus avoiding any ex ante commitment and ex post misallocation?
A key contribution of my paper is to answer this question. Suppose there is information
asymmetry between market lenders and the …rm, such that the former cannot observe
…rm quality. Suppose also that the bank has a superior monitoring capability, allowing
it to observe the quality of a …rm (see e.g. Diamond and Rajan (2001)) . If the bank
commits to lend to the …rm in the future, it can provide a signal of …rm quality to the
market. Market lenders will more readily lend to …rms, in the presence of this signal.
    In the absence of capital regulations, this signal would not increase surplus; without
a credit line, the …rm could still get …nancing from the bank in the form of standard
bank loan as long as the bank can observe …rm quality. However, in the presence of
capital regulations, the bank is constrained in the total amount of credit it can o¤er
even in the good state. By providing a signal to the market, the bank can ensure that
more …rms get …nancing in the good state than the number it could support on its own
balance sheet. It has an incentive to do this because, when they remain undrawn, credit
lines increase surplus via signalling but do not generate costs; this is because the bank
does not face a full capital charge on credit lines when they remain undrawn.
    The bank can extract some of this surplus by charging the …rm an ex ante upfront
…xed fee. This o¤sets the expected cost of a credit line in the bad state, which is the
cost to the bank of having to ration credit to other types of borrower, who do not hold
credit lines. In practice, a high proportion of bank revenue from credit lines comes
from fees which are paid on the ‘  undrawn’portion of the credit line (see Su… (2009) and
Loukoianova et al. (2006)).
    This motivation of credit lines is consistent with empirical evidence. Indeed, there
is signi…cant evidence of this signalling e¤ect (see Mosebach (1999), Loukoianova et al.
(2006)). As argued by Loukoianova et al. (2006), ‘      opening a credit line with a highly
reputable bank usually sends a positive signal to other …nancial market participants’       .
                                                                             s
Mosebach (1999) …nds evidence of a positive market reaction to a …rm’ stock on the
news that a credit line has been granted.4 The credit line is a credible signal because,
not only can the bank observe …rm quality, but it can make the credit line contingent
on …rm quality. In practice, credit line contracts require the …rm to …le reports to the
bank on a regular basis, even when the line is undrawn, and are contingent on the …rm
satisfying certain characteristics, such as solvency ratios.
(Chateau (2007) and International Monetary Fund (2008)). There is no capital charge for these com-
mitments, despite banks frequently honouring commitments in adverse conditions to avoid losing rep-
utational capital. (Bhalla (2008) see p.407)
   For longer term irrevocable commitments, the CCF is 50% and the PRF is 100% under both Basel
I and Basel II.
   4
                                                    s
     Mosebach (1999) also …nds evidence that a bank’ stock reponds positively to such news.



                                                2
    However, not all …rms can obtain credit lines. Typically, …rms who hold credit lines
must have at least a certain credit-rating level and visibility in the market (see Su…
(2009) and Loukoianova et al. (2006)). Credit lines play a key role as bargaining chips
for banks in competing for such …rms’custom. By contrast, for those …rms which are
dependent on loans from a speci…c bank, banks do not need to compete. As a result,
the bank has no need to provide contractual commitments to this latter type of …rm.
It is these …rms who will be rationed when drawdowns are high.
    By exploring this mechanism in a simple model, I highlight key policy implications,
both for monetary policy and capital regulations. I show that it is the interest rate in
the good state, rather than the bad state, which a¤ects the degree of misallocation in
the bad state. This is because it is the good state in which the credit lines generate
surplus, but no cost to the bank. I also show how changes in capital regulation may
a¤ect the degree of misallocation. If undrawn lines face a higher capital charge, relative
to drawn lines, the bank is forced to pay the cost of credit lines even when they are
not drawn. This can lead the bank to decrease its exposure, and therefore decrease ex
post misallocation in the bad state. In the limit, if the full capital charge on credit lines
                                                      s
were applied when they were undrawn, the bank’ optimal exposure would be set to
eliminate misallocation in the bad state. Furthermore, I derive implications for cyclical
capital requirements. If overall capital adequacy requirements are relaxed in the bad
state, meaning the bank has to …nd less capital for each new loan, this will reduce
misallocation ex post. This is despite the fact that the bank will increase its ex ante
exposure to credit lines.
    In the rest of the introduction, I present a summary of the model, followed by an
                                                                               y
explanation of how policy can a¤ect this ex post misallocation. I then brie‡ outline my
empirical work before concluding with a discussion of how this paper relates to existing
research on credit lines.

1.2     Summary of Model, Results and Empirical Motivation
The model operates over three periods, 0, 1 and 2. The agents in the model are …rms,
market lenders and a bank.5 At period 1, each …rm needs to borrow a …xed amount for
a given investment project, which will succeed or fail at period 2. I consider two types
of …rm; type 1 and type 2, where the latter are bank-dependent. Within each type, there
is a continuum of qualities; …rms vary in the amount of residual assets that would be
left if the project failed at period 2.
    For type 1 …rms, there are two frictions in obtaining …nancing from the market at
period 1. The …rst is asymmetric information; the market cannot observe the …rm’       s
quality (its potential residual assets) and is therefore unwilling to lend. The second
                          s
comes from the lender’ own ability to extract value from a given amount of residual
assets. At date 1, there is an aggregate shock and the state is revealed as either good
                                                                               s
or bad; the lender can either extract a high or a low value from a given …rm’ residual
  5
    Since the model focusses on a situation where banks behave perfectly competitively in o¤ering
credit lines, I analyse the optimal problem of just one bank in the model. I also abstract from any
interlinkages between banks, since this is not the focus of the paper. Such systemic e¤ects would
however be interesting to consider in further work.


                                                3
assets.6 This second friction means the market would be unwilling to lend in the bad
                                                                      s
state, irrespective of whether it had full information about a …rm’ quality.
    At period 0, the bank chooses how many …rms to which it will o¤er credit lines.
The bank will e¤ectively maximise social surplus ex ante at period 0. The credit line
increases social surplus since it enables the …rm to borrow at period 1, in both states,
when otherwise it would have been unable. However, part of the surplus comes from a
signalling role of credit lines. By committing to lend to the …rm if necessary, the bank
                    s
can learn the …rm’ true j and so provide a signal of …rm quality to the market. This
overcomes the asymmetric information mentioned above, enabling the …rm to obtain
market …nancing in the good state. As a result, the bank will o¤er more credit lines
than its balance sheet could support in the good state. In so doing, it increases social
surplus at period 0.
    In the bad state, however, all …rms with credit lines will draw on them; the high
                              s
drawdowns cause the bank’ capital adequacy constraint to bind. This causes a misal-
location of credit as the bank is constrained in its ability to lend to …rms without credit
lines (i.e. type 2 …rms). In the bad state, the marginal return to type 2 loans is greater
than the marginal return to loans via drawdowns.
    Ex post misallocation in the bad state is not surprising when we consider that,
ex ante, the bank maximises a weighted average of surplus in the good state and net
cost in the bad state. Ex ante the bank solves for the constrained …rst best allocation.
E¤ectively, it maximises surplus, taking capital regulations and monetary policy as given.
A key implication of the model, therefore, is that a change in policy can change the degree
of ex post misallocation in the bad state. It can do this by changing the ex ante optimal
allocation chosen by the bank.
    Policy can a¤ect the degree of ex post misallocation in the bad state. Perhaps
surprisingly, however, it can do so by a¤ecting the marginal bene…t of credit lines in the
good state. Why should this be the case? Misallocation in the bad state is given by
the wedge between the marginal bene…t of drawdowns in the bad state and the marginal
bene…t of foregone loans in the bad state. Ex ante, the bank only sets a wedge between
these because there is positive expected surplus from credit lines in the good state. Given
the signalling characteristic of credit lines, they generate surplus even in the state when
                                         s
they are not drawn down. The bank’ optimal condition can be summarised by

                  Pr(good)M B G (drawdowns) + Pr(bad)M B B (drawdowns)
                = Pr(bad)M B B (foregone loans)

Here, I use M B S to denote marginal bene…t in state S. As long as there is surplus in
                         s
the good state, the bank’ optimal exposure will be set so that misallocation, MA , will
be positive:

                    MA     M B B (foregone loans)-M B B (credit lines)       0
  6
    The amount of residual assets varies across …rms, but the amount of value that can be extracted
from a given set of residual assets varies across the state.




                                                4
This will mean that the amount of drawdowns, relative to foregone loans, is suboptimally
high in the bad state.7
    As a result, I show that it is the interest rate in the good state, rather than the
bad state, which a¤ects the degree of credit misallocation in the bad state. A lower
interest rate in the good state means banks anticipate a higher surplus per loan in the
good state. This increases the bene…t of credit lines, without increasing the cost, since
the cost is only experienced in the bad state when credit lines are drawn down. Banks
increase their supply of credit lines ex ante to capture this surplus. This leads to greater
misallocation of credit in bad state; it increases the wedge between the marginal return
to drawdowns in the bad state, and the marginal return to other loans in the same state.
This result resonates with arguments claiming low interest rates in the pre 2007 period
increased vulnerability to a crisis (Bank For International Settlements (2009) Part III).
Along the same lines, if agents place low weight on the likelihood of market turmoil,
banks will build up exposure and thus lead to high misallocation in the bad state.
    By contrast, a lower interest rate in the bad state has a symmetric e¤ect on the the
marginal return to drawdowns in the bad state, and the marginal return to other loans
in the same state. It increases the surplus from a drawdown in the bad state, but it
also increases the surplus from loans to other borrowers, who do not hold credit lines
and will be rationed by drawdowns. A lower interest rate in the bad state therefore has
an o¤setting e¤ect on the bene…t and cost of credit lines.
    With respect to capital regulation, I …nd that a signi…cant redistribution of capital
charges from drawn to undrawn lines would reduce misallocation in the bad state. This
is equivalent to imposing a high Credit Conversion Factor on undrawn lines (see footnote
on page 1). If the bank is forced to pay a high cost on undrawn lines, this will reduce
the expected surplus in the good state; the bank will have an incentive to reduce its
                                                           s
exposure ex ante. This supports the Basel Committee’ suggestion to impose a higher
CCFs on o¤ balance sheet items, such as credit lines (see Basel Committee on Banking
Supervision (2009)).
    Finally, I show that a loosening of capital requirements in the bad state will reduce
misallocation. This speaks to recent discussions about time varying capital regulations.
Ex post, banks will be less constrained by capital requirements for a given exposure to
credit lines. Although banks anticipate this loosening of policy, and thereby increase
their exposure ex ante, this is not su¢ cient to outweigh the bene…cial e¤ect.8
    In the …nal section of the paper, I explore whether there is any suggestive evidence in
the data that is consistent with the model. This is a …rst pass at exploring the empirical
interaction between capital and credit line exposure; as discussed in this section, I plan
a more complete exploration of this issue as further work.
   7
      Of course, there will also be suboptimal allocation in the good state, just the other way around.
However, in this paper I focus on the credit misallocation in the bad state. It seems reasonable to suppose
credit misallocation and rationing in a downturn may have more severe immediate macroeconomic
consequences. I leave the long term consequences of credit misallocation in the good state as a topic
for further research.
    8
      I do not consider broader questions of optimal capital regulation in this framework. This is because
I simply treat capital regulations as an exogenous constraint and do not consider the bene…cial e¤ects
of capital regulation. It would be interesting to consider this in further work.



                                                    5
    Consider the ratio undrawn credit lines ; this re‡
                              capital
                                                      ects exposure to credit lines, relative to
capital. Previous work has just looked at the liquidity aspect of credit line exposure
(Ivashina and Scharfstein (2009)). However, if the capital e¤ects I highlight are also
present, this ratio, calculated for the quarters before the shock, should be negative and
signi…cant. I present preliminary evidence to suggest that it is. Following Ivashina and
Scharfstein (2009), I use the collapse of Lehman as a key shock a¤ecting market credit
supply. Although we do not observe drawdowns in the dataset, there is substantial
evidence that this shock led to a reduction in available market …nancing, and thus
a¤ected credit line usage. As documented by Ivashina and Scharfstein (2009) and others
(e.g. Bank of England (2008b)), this shock to the market led corporates to increase their
drawdowns on existing credit lines.

1.3    Related Literature
This paper is related to two strands of the literature on credit lines. The …rst explores
the motivation behind credit lines, focusing largely on the contract between the …rm
and the bank. Holmstrom and Tirole (1997), Holmstrom and Tirole (1998) and Boot
et al. (1987) use agency problems to motivate why there may be demand for a credit
line. Su… (2009) and Yun (2009) empirically examine the role played by credit lines in
…rm …nancing. In a similar spirit to my paper, Kanatas (1987) argues that, if …rms’
credit risk is unobservable, loan commitments (i.e. credit lines) can be purchased by
…rms to reveal their type, and thus can be used as a signal in the sale of commercial
paper. However, the author largely focuses on optimal contracting in the presence of
adverse selection, and does not examine the wider impact of drawdowns on the bank’      s
balance sheet and capital adequacy.
                                                                        s
      On the whole, these papers focus almost exclusively on the …rm’ demand, and do
                   s                                                      s
not link the bank’ supply of a credit line with other elements of a bank’ lending portfo-
lio, or capital requirements. With the exception of Kanatas (1987), they do not model
credit lines as an outside option to market borrowing. Explaining the coexistence of
credit lines and market lending is important when considering macroeconomic questions
of credit allocation.
    The second strand in the literature explores the interplay of credit lines and banks’
deposits. Kashyap et al. (2002) focus on the liquidity risk to which credit lines expose
a bank. They argue there are synergies between deposit-taking and the provision of
loan commitments, as long as withdrawals and drawdowns are not perfectly positively
correlated. Gatev and Strahan (2006) extend this point, by arguing there is in fact a
negative correlation between withdrawals and drawdowns. More recently, Ivashina and
Scharfstein (2009) and Cornett et al. (2010) show how banks respond to such liquidity
risk in the context of the recent crisis. This strand of the literature does not focus on
the demand for the credit line or the role of capital requirements.




                                               6
2     The Model
The model operates over three periods, periods 0,1 and 2. The agents consist of banks,
perfectly competitive market lenders, and also entrepreneurial …rms. As mentioned
above, there are two types of …rm, type 1 and type 2. The latter will be bank-dependent
                                                                        s
…rms, but face similar investment needs to type 1 …rms. For now, let’ consider type 1
…rms.
    At period 1, these …rms will require project …nancing. They have no internal funds
for investment, so seek funding from perfectly competitive market lenders. The per
unit cost of …nancing is is , where s denotes the state. We take is to be exogenous,
in‡ uenced by monetary authorities (see later policy discussion), but known by agents
with perfect foresight. Firms require a unit investment for a project which will succeed
with probability p and return R at period 2. With probability (1 p) the project will
fail. In this case, some residual assets remain. We assume residual value varies across
…rms, j , and is privately observed by the …rm at the beginning of period 0. The net
present value (NPV) of the project for …rm j in state s is given by

                                    pR + (1       p)   j   is

    Residual assets play an important role in the model for two reasons. First, their value
is unobservable to the public, i.e. to market lenders. In the absence of an accurate signal
of such value, market lenders will ration credit to …rms. Second, residual assets are
partially illiquid, such that lenders cannot extract their full value. So, even if their true
value was perfectly observed, only some fraction s of that value could be pledgable to
outside lenders, where depends on state s. The …rst of these characteristics motivates
the signalling role of credit lines. The second of these characteristics provides the basis
for understanding an aggregate shock; in the good state, residual assets are relatively
more pledgable than in the bad state. This means credit rationing is relatively more
severe in the bad state (irrespective of whether an accurate signal of residual value is
observed).
    Before discussing the model in further detail, here is the timeline:




                                              7
2.1      Motivation for credit lines
I assume the market cannot observe the residual asset value of any given …rm at period
1.9 This asymmetric information leads to market rationing. I suppose type 1 …rms can
be of ‘high’or ‘ low’quality. If the …rm is a low quality, its residual assets are worthless.
If the …rm is of high quality, it has positive residual assets. Residual asset value for high
quality …rm j will be denoted as j . These high quality …rms are uniformly distributed
along a continuum in j , over the interval [ ; ], where              = 1. The table below
summarises this point:

       Type 1 …rms
                            Residual Assets
       Low quality …rm           j = 0
       High quality …rm       j    U[ ; ]

    Throughout the paper I focus on high quality …rms. However, the presence of low
                                  s                                  s
quality …rms means the market’ expectation of a high quality …rm’ residual assets will
                                                                         s
be signi…cantly lower than the true value. To formalise the market’ expectation at
period 1, suppose that proportion v of type 1 …rms are of high quality, where v < 1.
                                                                              +
The market’ expectation of residual assets for any given …rm is therefore v[ 2 ]. For v
             s
su¢ ciently low, the loan will have negative net present value (NPV) for the market, even
in the good state, and even if residual assets are fully pledgeable to outside investors.
In other words,
                                         +
                        pR + (1 p)v[         ] < is    for s = G; B
                                         2
    So market lenders will not provide loans to any …rm. Note this means some …rms,
with positive NPV projects, are nevertheless rationed as long as the following condition
holds for some :

                                       pR + (1      p)   j   > is
     However, credit lines can be used as a signal of quality to the market, thus overcoming
this information asymmetry. At period 0, in advance of investment requirements, …rms
can sign credit lines with a bank, upon paying an upfront …xed fee (discussed later).
This will be a commitment to lend to the …rm, should it require bank …nancing. As
discussed in the introduction, the bank has a monitoring technology which enables it to
observe the true value j after it has signed the credit line, at the end of period 0. I
assume the bank can make the credit line contingent on the value of j , and will revoke
it if the …rm turns out to have misrepresented its j . As a result, if a …rm has a credit
line in place by period 1, the market can correctly infer the value of j from the speci…cs
of the contract; the presence of the credit line is a credible signal since the bank has
committed to lend to the …rm.10
   9
     For simplicity, I assume that the true residual asset value is observed at period 2.
  10
     Of course, the bank could deliberately fail to revoke a credit line where the …rm has zero residual
asset value, thereby misleading the market into lending; this might enable the bank to extract undrawn
fees from that …rm. However, as we will see, the bank will set the credit line contingent on an observed



                                                   8
                                                  s
    The key point is that, by signalling a …rm’ quality via the presence of the credit
line, the bank can ensure that not all …rms draw down in the good state. Given the
bank receives a …xed fee from the …rm, regardless of whether the …rm draws down, the
bank has an incentive to o¤er a large number of credit lines. It will therefore o¤er more
credit lines than it could support on its balance sheet in the good state.
    I assume that the bank behaves perfectly competitively in o¤ering credit lines.11 In
expectation at period 0, therefore, the bank will break even on each credit line. At this
point, the bank will also choose its optimal exposure to credit lines; it will choose the
lowest quality …rm c with which it will sign a credit line.
    In signing a credit line, we assumed the bank develops a relationship with the …rm,
enabling the bank to extract information about the …rm and its projects. This enables
the bank to observe the true residual value, once it has signed the credit line. In practice,
banks do obtain signi…cant information about the …rm during periods when a credit line
is undrawn. Typical covenants in credit line contracts require …rms to submit quarterly
or monthly …nancial statements to the bank, as well as preventing the …rm from mak-
                                                   s
ing changes to management without the lender’ permission (see Financial Leadership
Exchange (2008)). Banks are also able to observe small but frequent drawdowns for
inventory purposes. Whilst distinct from the size of drawdowns motivating this model,
they do enable the bank to obtain information about the …rm’ activities.12
                                                                  s
    Whilst agents can contract on the basis of observed payo¤s and value, we assume they
cannot contract on the state of the world. This is consistent with empirical observation.
While credit line covenants tend to be contingent on …rm speci…c characteristics, their
revokability is not contingent on aggregate activity or states. We therefore assume the
state is non-veri…able (see Hart and Moore (1998)). This is a common assumption in
the literature (see Houston and Venkataraman (1996)). The exact nature of the state
may be observed with delay - at least, veri…able characteristics of the state may be
observed only after credit lines are drawn down (see Jovanovic and Ueda (1997) and
Meh et al. (2010)). Indeed, in the recent crisis, the exact extent of credit supply and
credit rationing has only been observed with any accuracy with some delay (via surveys
etc). Of course, since we allow for di¤erent costs of funding across the two states (is ),
this means we assume a court could not immediately observe and verify the state by is ;
indeed, the cost of funding faced by a lender is observed by himself, but not immediately
by outsiders, in particular the courts.
value c where c > > 0. As long as is observed before the state of the world is revealed, the bank
has no incentive to fail to revoke a credit line where < c .
   11
      This does not mean the bank behaves perfectly competitively in all markets. In particular, as we
will see, it has a monopoly over type 2 …rms which are bank-dependent.
   12
                                                           smaller and less visible’…rms who bene…t from
      As Loukoianova et al (2006) observe, it is typically ‘
signals provided by credit lines. Larger …rms, who are more inherently visible, may have less need for
such signals. However, by that argument, these …rms are inherently less likely to require credit line
funds, even in the presence of market shocks. The credit line holders we therefore model here are those
smaller, less visible …rms.




                                                   9
2.2     Asset liquidity
Of those residual assets, some fraction will be liquid and thus pledgable to outside
lenders. The remaining fraction will be illiquid and thus unpledgable. At period 1,
there is an aggregate shock to the liquidity of those assets. This shock will produce
either a good state or a bad state (s = G; B). In state s, a fraction s of residual assets
will be su¢ ciently liquid such that they are pledgable to outside lenders, in the event of
project failure. The remaining fraction (1      s ) will be illiquid and nonpledgable. The
good state represents a situation of greater liquidity and thus greater ease of credit: a
higher fraction of residual assets are pledgable ( G >> B ). The good state occurs
with probability q and the bad state with probability (1 q).
    Since we assume G >> B , this means credit rationing is signi…cantly worse in the
bad state. For simplicity, we assume B is so low that loans to all …rms will be negative
NPV. In other words, we assume:

                                   pR + (1      p)    B    iB < 0,                                  (1)
    In the bad state, therefore, the market will not lend to any …rm.
    In the good state, we assume G is su¢ ciently high such that the market will lend
to those …rms with credit lines. A su¢ cient condition for this is

                                    pR + (1      p)   G    iB > 0                                   (2)

    Note it will not lend to a …rm without credit lines, even if             j   > , since there is no
                      s
signal of such a …rm’ quality.

2.3     Bank Dependent Loans and Capital Adequacy Require-
        ment
I now consider type 2 …rms. I assume they are each dependent on loans from a speci…c
bank. For instance, cash ‡   ows or projects of the …rm may be unobservable to the market,
and only observed by the bank with whom the …rm has a long-standing relationship.
This is particularly the case for small or medium sized enterprises, whose public presence
is minimal. Since they are bank-dependent, the bank does not need to provide then
with credit lines, in order to compete for their custom. For simplicity I model type 2 …rm
project payo¤s as identical to that of type 1 projects, with type 2 …rms also uniformly
distributed on a continuum in , on the interval [ ; ]. Whilst this is not necessary for
the results, it helps with tractability.
    The bank also faces a capital adequacy requirement (CAR). In particular, we assume
the bank must hold capital w at least equal to fraction k of its risky assets.13 If we denote
quantity of drawn credit lines as Qs and quantity of bank dependent loans as L(is ), then
the CAR is:
  13
    There is no bank default in this model. We are implicitly assuming the bank has a high cost of
default. This cost must be su¢ ciently high such that the bank would rather constrain its lending if the
CAR binds, than choose to have insu¢ cient capital and risk regulatory sanctions and possible default.




                                                  10
                                    k[Qs + L(is )]   !
    I assume capital is …xed. This captures the idea that, at least over short run periods,
a bank may face costs to increasing capital. I also suppose that bank loans to type 2
…rms are not subject to the aggregate shock. In other words, the amount of residual
assets the bank can extract from type 2 …rms does not vary with the state. Whilst the
strength of this assumption is not vital to the model, it is necessary that the pro…tability
of bank dependent loans does not decrease by the same extent as market loans in the
bad state. Otherwise, the increase in drawdowns of credit lines will be completely o¤set
by a reduction in optimal lending to bank dependent …rms, and the bank will not face
a binding capital constraint in the bad state.
    All this amounts to the following: the pool of bank dependent …rms is less sensitive to
the market shock than the pool of non-bank dependent …rms. This is not unreasonable
and can be motivated in a number of ways. One interpretation of the market shock
to pledgability is that it represents illiquidity of secondary markets, in which the lender
                         s
hopes to sell the …rm’ collateral, and thereby extract value. It seems reasonable to
suppose the collateral of small, non publicly listed …rms is of a di¤erent nature, and not
necessarily traded on secondary markets. Alternatively, given these …rms are already
dependent on speci…c banks for funding, it seems reasonable to suppose the bank has
engaged in some earlier monitoring; as part of this process, the bank would have excluded
at least some of the …rms who are likely to su¤er following an aggregate shock. A third
interpretation is that, given these …rms are bank dependent, the bank may be able to
extract at least some of their illiquid residual assets (see Diamond and Rajan (2001)).
This could easily be modelled with a simple extension to the model. In which case,
variations in the liquidity of these assets will not greatly a¤ect the pro…tability of bank
loans to such …rms.
    To simplify the model, therefore, we simply assume the bank can extract all residual
assets from type 2 …rms, regardless of the state; a partial relaxation of this assumption
would have only quantitative, not qualitative, e¤ects on the results.

2.3.1   Credit Line drawdowns vs Market loans
We have already highlighted that the bank, in setting optimal supply of credit lines, will
o¤er more than it could support in the good state, given its CAR. It anticipates that
its CAR will not bind in that state because it knows …rms can always obtain market
…nancing in that state. For the purposes of solving for the optimal supply, therefore, it is
not important to specify the exact amount of …rms that draw down in the good state. At
period 0, the bank can always set the face value of the loan (via a drawdown) such that
a …rm prefers market …nancing. Indeed, since market lenders are perfectly competitive,
the …rm can always extract full project surplus by going to the market. Although we
do not solve for the face value, as it does not a¤ect optimal exposure (see below), there
is no reason in the model why the bank would wish to set a lower face value than the
market. From the preceding argument, therefore, it is clear that as long as the market
                                                            s
stands ready to lend to …rms in the good state, the bank’ capital adequacy constraint
will not bind in that state, in equilibrium.


                                            11
     For ease of exposition, however, we assume there is an epsilon deadweight cost of
bank …nancing, relative to market …nancing. This ensures that, ex ante, the terms of the
credit line will be set such that no …rm will draw down unless unable to obtain market
…nancing; in other words, the optimal contract will minimise deadweight costs. Indeed,
it is consistent with empirical evidence, which suggests …rms would rather seek market
…nancing than bank …nancing. Nevertheless, given the argument above, this assumption
does not a¤ect the results; it simply ensures a clearer discussion of the model.

2.3.2      Good state: CAR does not bind
Given the preceding argument, the CAR will not bind in the good state as long as the
unconstrained optimal level of loans Lunc are such that
                                                         !
                                              Lunc <                                                (3)
                                                         k
    Given the bank has monopoly power over type 2 …rms, we assume for simplicity it
extracts the whole surplus of each project. So unconstrained loans to type 2 …rms are
given by
                                     Lunc =
       So condition 3 will be satis…ed as long as
                                                         !
                                                     <
                                                         k

2.3.3      Bad state: CAR binds
Whether or not the CAR binds in the bad state will depend on the minimum level of
  j against which the bank commits to provide a credit line c . Recall that all …rms will
draw down in the bad state, since they have no option to borrow from the market.
    By increasing c at period 0, the bank can reduce the amount of loans supplied via
credit lines at period 1, which will relax the CAR constraint at the margin in the bad
state.
    It is helpful to consider the optimal value of c in the absence of the CAR constraint.
This will simply be given by , since we assume all projects have positive NPV for …rms
  j > . We consider a case in which pledgeability is so low in the bad state (i.e.      B
is low) that CAR will bind for credit line drawdowns, evaluated at . In other words,
choosing c = could never be an equilibrium.14 We therefore assume

                                                             !
                                         QB ( ) + Lunc >                                            (4)
                                                             k
                                                             !
                                     (      )+(          ) >
                                                             k
  14
    At this point, we can see why it is important that the marginal bene…t of lending to non-credit line
holders does not decrease 1:1 with the increase in drawdowns. Indeed, if Lunc were to decrease in the
bad state, relative to the good, by the same extent as the increase in drawdowns, the CAR would not
bind in the bad state.


                                                  12
       Given that the CAR binds, type 2 loans will simply be given by
                                                                       !
                                        QB ( c ) + L( c ) =
                                                                       k
       where
                                             QB ( c ) =            c

       and

                                                                  B
                                             L( c ) =             bd
                   B
       such that   bd   is determined by the binding CAR constraint:15


                                        B                                  !
                                        bd    =           c   +
                                                                           k
                                                                   !
                                              = 2             c
                                                                   k

2.4          Contract: fees
Since loans in the bad state will be negative NPV for the bank, the bank will have to
charge a …xed fee F in order to break even in expectation16 . The optimal contract will
also specify Rc , the face value of the loan in the event the line is drawn. Once again, this
re‡ects empirical reality. Typically, a credit line contract will specify an interest rate to
be paid on any drawdown, plus a commitment fee paid for the portion of the line that
remains undrawn, e.g. in the good state, and/or an upfront …xed fee (see Loukoianova
et al. (2006)).
    However, although we include Rc and F in our discussion below, we do not need
to solve for them, nor do they a¤ect our results.17 In fact, as we will see below, we
cannot determine each of them uniquely. Yet this is not a problem: since Rc and F are
just transfers between the bank and the …rm, they do not a¤ect the optimal condition
determining the amount of credit line exposure c . This is because c is set to e¤ectively
maximise social surplus.
  15
      Note that I have set up the problem so the CAR does not bind in the good state. However, even
if it did bind in the good state, it would bind less tightly than in the bad given B < G ; i.e. it would
bind less tightly as long as drawdowns were greater in the bad state compared with the good state. In
this case, there would still be a misallocation result in the bad state because the marginal bene…t of
drawdowns in the bad state would still be less than the marginal bene…t of bank dependent loans.
   16
      We can assume the …rm has no liquid assets at period 0, so must borrow to pay this …xed fee. It
will then have to rollover this loan at period 1, a¤ecting the total borrowing requirement in that period.
   17
      For completeness, however, it is worth mentioning the following constraints which will apply to F
and Rc . Clearly, Rc must be feasible, so Rc R; the …rm must have su¢ cient funds to pay the face
value of debt in the event of project success. Regarding F ; if the bank wants to ensure the …rms is able
to obtain market …nancing in the good state, it will not set F so high that rolling over the loan for F
at period 1 causes the market to ration a …rm. In other words, F will be set so as to avoid violating
the following condition:
                                     pR + (1 p) G j iG (1 + F ) 0
  In what follows below, we focus on cases in which these constraints do not bind.


                                                    13
2.5       Optimal credit lines
The optimal credit line contract at period 0 will maximise expected …rm surplus from
                                   s
credit lines, subject to the bank’ participation constraint. In choosing c , the bank
faces a tradeo¤. A lower c (i.e. higher exposure) means that overall returns from credit
lines are higher in the good state. However, a lower c also means that lending to bank
dependent …rms is further away from the optimal level when the CAR binds in the bad
state.
                                                                  s               s
    The bank will make zero pro…ts in expectation on each …rm’ credit line: it’ par-
ticipation constraint for each …rm will therefore bind. Given c , each individual par-
ticipation constraint will jointly determine Rc and F . Since we are only interested in
determining c , we consider the sum of all these participation constraints. Likewise, we
consider the sum of all …rms’objective functions. As a result, Rc and F will drop out
of the optimal problem determining c . In what follows, we focus on these aggregated
functions.
    The aggregate objective function for the …rms contemplating signing a credit line is
therefore:
                            Z
                   f(1 q)       [pR + (1 p)     iG ]d g                               (5)
                                           c
                                 Z
                           +fq           [p(R        Rc ) + (1    p)(1            B)     ]d g   F[        c]
                                     c


    The …rst line is the expected net bene…t in the good state, from holding a credit line.
The second line is the expected net bene…t in the bad state, from holding a credit line.
Note that in the absence of a credit line, the …rm would have zero payo¤ in both states,
because the …rm would be unable to obtain …nancing; no one would observe its true j .
    In the good state, the …rm receives funding as long as > c ; i.e. as long as he holds
a credit line. Since market lenders are competitive, the …rm extracts the surplus from
the project in the good state, net of the costs of …nancing.
    In the bad state, the …rm holding a credit line will still be rationed by the market18 .
The …rm will however be able to draw down its credit line as long as residual asset value
is positive. Given the setup of the model the bank can only extract pledgeable assets
in the event of project failure. Therefore, the …rm will always obtain (1        B ) in the
bad state, in the event of project failure. We can think of this as non-pledgable income.
               s
    The bank’ (aggregate) participation constraint is given by
                                Z
                 F[      c] + q   [pRc + (1 p) B       iB "]d                           (6)
                                                c
                       Z                                                  Z
                   q        (pR + (1            p)       iB )d        q                 (pR + (1     p)    iB )d
                                                                              unc ( )
                                                                              bd    c


                              s
    Condition 6 is the bank’ participation constraint. Given banks behave competitively
                                 s
in o¤ering credit lines, the bank’ participation constraint will bind in equilibrium. Note
 18
      This follows given condition (1).


                                                                 14
that the right hand side is equal to the expected foregone pro…ts on bank dependent
loans due to credit line commitments. Since these foregone pro…ts are positive, it must
be that the left hand side is positive. In other words, the bank must make positive
expected pro…ts on credit lines, equal to expected foregone pro…ts on bank dependent
loans. On the left hand side, the …rst term is the revenue the bank receives from the
…rm in the good state19 .
                           s
    Substituting the bank’ aggregate participation constraint into the aggregate objec-
tive function allows us to solve for c .
                       Z                             Z
         max (1 q)        [pR + (1 p)      iG ]d + q    [pR + (1 p)      iB "]d (7)
              c
                              c                                                    c
                   Z                                               Z
              fq       (pR + (1       p)         iB )d         q                 (pR + (1   p)       iB )d g
                                                                       unc ( )
                                                                       bd    c


    This shows we can characterise the optimal exposure to credit lines, c , independently
of the optimal values of Rc and F . Indeed, the optimal exposure is found by maximising
overall net surplus of credit lines: notice that the function (7) is simply net surplus from
credit lines.
    At this point, it is worth mentioning the bank will strictly prefer to issue credit lines
to all …rms in the range c ! . In other words, it would not choose to o¤er bank loans
for some range      ! , and credit lines to the remainder c ! . I show this in the
appendix. Intuitively, any …rm in this range is prepared to pay a higher …xed fee than
the cost the bank would face from having committed itself via a credit line.


3       Results
The …rst order condition for               c   is given by

              0 =        (1   q)[pR + (1              p)   c       iG ]     q[pR + (1       p)   c   iB   "]
                                                                    !
                        +q(pR + (1             p)[2        c          ]     iB )
                                                                    k
       So
                                               (qiB + (1 q)iG ) pR + q"
                                  c   =
                                                     [(q + 1)(1 p)]
                                                                     !
                                                 q(pR + (1 p)[2      k
                                                                       ] iB )
                                               +
                                                         (q + 1)(1 p)

3.1         Credit Misallocation
What does a given level of exposure c mean for the degree of credit misallocation in
the bad state? Before we consider comparative statics, it is helpful to recall what we
  19
    The …xed fee F is e¤ectively written in future value terms, since all terms in the optimal problem
are written in terms of value at period 2.


                                                               15
mean by misallocation. Suppose there was an optimal allocation of credit in the bad
state; then the marginal bene…t of drawn credit lines would equal the marginal cost of
foregone bank dependent loans. Using MA to denote misallocation in the bad state,
therefore, we write

         MA      M B B (bank dep. loans)-M B B (credit lines) 0
                                         !
               = [pR + (1 p)(2       c     ) iB ] [pR + (1 p)                           c     iB   "]
                                         k
   where M B s (n) represents marginal bene…t of n in state s.
   We can also show that the degree of misallocation in the bad state depends on the
surplus in the good state. Note that the …rst order condition for c can be rearranged
and written as
                               (1       q)
      M B B (credit lines) +                 M B G (credit lines)           M B B (bank dep. loans)=0
                                    q
   We therefore have the following lemma:

Lemma 1 Misallocation in the bad state is a function of the marginal bene…t of credit
lines in the good state:



                  MA      M B B (bank dep. loans)-M B B (credit lines)
                          (1 q)
                        =         M B G (credit lines)
                            q
                          (1 q)
                        =         [pR + (1 p) c iG ]
                            q
    As long as there is positive surplus generated by the signal from credit lines in the
good state, the optimal exposure to credit lines will be set so that there is misallocation
of credit in the bad state. In other words, too few loans will go to bank dependent
…rms, and too many to credit line holders, relative to the …rst-best.
    An increase in exposure (i.e. decrease in c ) does not, per se, lead to greater mis-
allocation. However, changes in certain parameters, such as q and iG , can exacerbate
this misallocation.

3.2    Change in q, the probability of the bad state
Lemma 2 As the probability of the bad state decreases, banks have greater incentive to
increase their exposure to credit lines:
                                                              !
              @ c   [pR + (1            p)(2         c        k
                                                                )    iB ]   (iG   iB ) + "
                  =                                                                          >0
              @q                                [(q + 1)(1          p)]




                                                         16
   Note this condition is positive as long as (iG iB ) is not too large relative to the
pro…ts made on bank dependent loans. This is reasonable; it simply means there is
some de facto limit to the range of interest rates which can be set by the monetary
authorities.20
   The key question, however, is whether this increased exposure translates into greater
credit misallocation in the bad state of the world? It turns out that it does.

Proposition 3 As the probability of the bad state decreases, there is an increase in
misallocation of credit in the bad state of the world:



                   @MA   M B B (bank dep. loans) M B B (credit lines)
                       =                        -
                    @q              @q                   @q
                                  @ c          @ c
                       =  (1 p)         (1 p)
                                  @q           @q
                                   @
                       =  2(1 p) c < 0
                                   @q
    As the probability of the bad state decreases, this will lead banks to build up greater
exposure to credit lines. This makes intuitive sense: the bank will put low weight on
the cost of credit lines when q is low. This is because the cost of drawdowns, in terms
of foregone other lending, only occurs in the bad state.

3.3     E¤ect of policy: change in interest rates
In the model we have taken the cost of funding to be exogenous, yet allowed it to vary
across the states. Whilst we will not impose any further structure on these rates, it
seems reasonable to suppose they are a function of monetary policy in each state.21 By
exploring comparative statics for iG and iB ; we can therefore make qualitative statements
about the e¤ect of monetary policy in the two states. Given the set up of the model, the
interest rates in each state are fully anticipated at period 0. In what follows, therefore,
we examine the e¤ect of the fully anticipated monetary policy.
    Perhaps surprisingly, it is the anticipated policy stance in the good state, rather than
the bad, which has an e¤ect on credit misallocation in the bad state.

Lemma 4 If agents anticipate a relatively low interest rate in the good state, this will
lead banks to increase their exposure to credit lines.

   To understand this, consider the e¤ect of a lower iG on surplus in the good state.
Since iG is the per unit cost of funds in the good state, a lower iG means higher surplus
  20
    This would be in‡  uenced by other factors in the economy, external to the model.
  21
    Costs of funding in each state will also depend on liquidity risk, counterparty risk etc. We do not
focus on these issues here; we only examine the marginal e¤ect of policy across the two states.




                                                  17
for a given level of c in the good state. As a result, the marginal bene…t of credit lines
increases, giving banks the incentive to increase exposure (i.e. decrease c ).

                                    @ c        1 q
                                        =                        >0
                                    @iG   [(q + 1)(1       p)]

    Again, we have to consider the e¤ect of this on misallocation.

Proposition 5 If agents anticipate a relative low interest rate in the good state, this
will lead to greater misallocation of credit in the bad state:

                 @MA    @M B B (bank dep. loans) @M B B (credit lines)
                      =
                  @iG              @iG                   @iG
                                 @            @
                      =  (1 p) c (1 p) c
                                 @iG          @iG
                                  @ c
                      =  2(1 p)        <0
                                  @iG

    As this shows, a decrease in iG will lead to an increase in MA : there will be greater
misallocation of credit. So a credible commitment by the authorities to keep interest
rates low in the good state will actually lead banks to build up high exposure to credit
lines, resulting in greater misallocation of credit in the bad state. Again this is because
a decrease in the interest rate in the good state increases the surplus from credit lines
in the good state. This drives a wedge between the marginal bene…t of credit lines in
the bad state and the marginal bene…t of foregone loans in the bad state.

Proposition 6 The expected interest rate in the bad state has no e¤ect on credit line
exposure.



                           @ c         q                         q
                               =
                           @iB   (q + 1)(1           p)    (q + 1)(1     p)
                               = 0

    To see this, note that a higher iB will decrease the marginal bene…t of credit lines
in the bad state, but will also decrease the marginal bene…t of bank dependent loans by
the same amount. So iB has no a¤ect on ex ante exposure or ex post misallocation.22
  22
     If we had modelled the bad state slightly di¤erently, such that only some, but not all, credit line
holders were rationed by the market, then iB would a¤ect c . This is because the degree of market
rationing would a¤ect the number of bank dependent loans that could be o¤ered, thus a¤ecting the
CAR constraint. If we denote by B the marginal …rm facing market rationing in the bad state, then
                                    m
 B
 m must be a function of iB . Furthermore, the marginal bank dependent loan would be a function
of B , and thus of iB . However, a decrease in iB , although causing an increase in exposure, would
     m
actually decrease misallocation in the bad state. This is because it would decrease market rationing in
the bad state, and so relax the CAR constraint at the margin: this would decrease the marginal cost
of credit lines in the bad state.



                                                  18
3.4     E¤ect of policy: increase in capital requirements
We now turn to consider the implications for capital regulation. This can be broken down
into two aspects. First, what is the e¤ect of changing the way in which speci…cally credit
lines are regulated? If banks had to put aside a larger amount of capital to support
undrawn lines, would this decrease credit misallocation in the bad state? Second, what
happens to misallocation if the total capital charge faced by the bank is reduced in the
bad state?23

1: Increase in ex ante capital charges on credit lines What if the capital charge
speci…c to credit lines were to change? In other words, what if undrawn credit lines
faced a positive capital charge - such that drawdowns did not result in such a large shock
to capital requirements? Consider [0; 1]: if fraction           k of undrawn lines must be
met in capital at the point of signing the line (period 0), then a subsequent drawdown
of this line only requires the bank to …nd an extra fraction, (1         ) k, in capital. In
this context, may be interpreted as the Credit Conversion Factor (CCF) (see footnote
in the introduction). In practice, ranges from 0 to 50% for credit lines under Basel I
and Basel II.
    To analyse a change in , we need to consider how available capital at period 0
relates to that at period 1. It seems reasonable, given the static nature of the model,
to continue with the assumption that capital is …xed for the duration of the game. I
leave consideration of varying capital to further work, in which I intend to embed this
model in a repeated game framework.
    Given ! is …xed throughout, a proportional capital charge at period 0, amounting
to kQB ( c ), simply decreases the available capital at period 1. This means the CAR
constraint in the bad state is the same as before. Although the bank only has to …nd
(1     )kQB ( c ) capital at period 1, it has less available capital with which to meet this
charge. So
                      k[(1     )QB ( c ) + L(iB ; c )] !       kQB ( c )
reduces to
                                    k[QB ( c ) + L(iB ;    c )]   !
                         s
   For low , the bank’ exposure to credit lines remains unchanged, as does the extent
of misallocation in the bad state. However, if is su¢ ciently high, the CAR will begin
to bind in the good state, as well as the bad. As a result, the bank will change its
optimal exposure. To see this, consider the CAR in the good state:

                                    kLunc (iG )    !      kQB ( c )

Although there are no drawdowns in this state, the available capital is reduced by the
charge on undrawn lines. For su¢ ciently large, this will bind. Indeed, if = 1, then
this constraint will be identical to that in the bad state.
  23
    We are ignoring issues of risk-weighting. Since all the assets are risky in this model, we focus, for
simplicity, on a simple fraction of these assets in de…ning capital charges.




                                                   19
    At a point where the CAR binds in the good state, the …rst order condition for                                              c
will be given as follows:
           0 =            (1   q)[pR + (1           p)      c    iG ]            q[pR + (1               p)     c    iB    "]
                                                                             B
                                                 B                   @       bd ( c )
                          q[pR + (1      p)      bd ( c )       iB ]
                                                                             @    c
                                                                                             G
                                                            G                            @   bd ( c ;         )
                          (1   q)[pR + (1           p)      bd ( c ;     )        iB ]
                                                                                              @      c
           B                                                             G
  where         is given as before and now
           bd ( c )                                                      bd ( c ;        ) is determined by the binding
CAR in the good state:
                                      G                 !
                                      bd ( c ;     )=           +(               c)
                                                        k
   Di¤erentiating this function with respect to , we obtain
                                                                                                          !
                @     c        (1     q)fpR + (1 p)[ + 2(      c)                                         k
                                                                                                            ]       iG g
                           =                                                                              2]
                @                       [(1 p)(1 + q) + (1 q)(1 p)
                           > 0
   An increase in will decrease exposure (i.e. increase                                       c ).       Therefore an increase in
  will decrease misallocation through its e¤ect on c .
Proposition 7 For su¢ ciently high capital charges on undrawn lines, an increase in
the proportion of capital charge to be paid on undrawn lines will lead to a reduction in
misallocation in the bad state;
                  @MA        M B B (bank dep. loans) M B B (credit lines)
                         =                            -
                   @                    @                     @
                                        @ c
                         =     2(1 p)       <0
                                        @
    For given exposure c , and overall capital requirement k, an increase in will increase
the proportion of capital charges paid on undrawn lines. For large , the bank e¤ectively
has to pay the cost in the good state as well as the bad. As a result, the bank will
reduce its exposure to credit lines, thus reducing misallocation in the bad state. This
supports the proposal made by the BCBS, in December 2009, to consider using a 100%
Credit Conversion Factor on o¤ balance sheet items for calculating the new leverage
ratio in Basel III (Basel Committee on Banking Supervision (2009)).
Proposition 8 If the bank had to pay full capital charges on undrawn lines, there would
be no misallocation of credit in the bad state
    This is equivalent to the case where                                   s
                                             = 1. In this case, the bank’ CAR will
bind equally in both states, regardless of the actual amount of drawdowns. The bank
will therefore set its optimal exposure such that the marginal bene…t of credit line
drawdowns in the bad state is equal to the marginal bene…t of foregone loans in the bad
state. Algebraically, this equates to

                                                      c   =      bd ( c )



                                                                20
2: Decrease in overall capital charge in the bad state We now consider a
decrease in overall capital requirements in the bad state. This relates to discussions
surrounding cyclically adjusted capital requirements. Recall the CAR constraint:

                                         k[Qs + L(is )]     !
    Here, k is the fraction of assets against which capital must be held. As k decreases,
the capital charge decreases. If agents expect capital requirements to be eased following
a bad shock, this is equivalent to a lowering of k in the present model, in the bad state.24
    On the one hand, an decrease in k decreases misallocation in the bad state for a
given level of exposure ( c ). This is because a decrease in k makes the CAR bind less
tightly for a given level of credit line drawdowns. On the other hand, at period 0, the
bank anticipates a lower k and therefore chooses higher optimal exposure to credit lines
(higher c ) since
                                   @ c        q     !
                                        =[         ] 2 >0
                                    @k     (q + 1) k

Proposition 9 A reduction in capital requirements in the bad state will reduce misallo-
cation in the bad state. This is despite the fact that the bank will increase its exposure
in response to an expected loosening of capital requirements in the bad state.



                  @MA   @M B B (bank dep. loans) @M B B (credit lines)
                      =                          -
                   @k              @k                     @k
                                !    @ c           @ c
                      = (1 p)[ 2         ] (1 p)
                                k    @k            @k
                                !     @ c
                      = (1 p)[ 2 2        ]
                                k     @k
                                       q     !
                      = (1 p)[1 2           ] 2 >0
                                    (q + 1) k

    A decrease in k will lead banks to increase their exposure ex ante, since they will
anticipate lower misallocation ex post. However, this increase in exposure will not
be su¢ cient to outweigh the bene…cial e¤ects of relaxing the constraint ex post (by
decreasing k). Indeed, the …rst e¤ect always dominates, since q < 1. Intuitively, the
      s
bank’ weight on the bad state, including any relative gain in the bad state, is always
less than 1. Overall, there will still be lower misallocation in the bad state, if k is
expected to be lower in the bad state.25 This lends support to the arguments in favour
of cylically adjusted capital requirements.
  24
     Note that a decrease in k in the bad state, as modelled here, has the same e¤ect as a decrease in k
in both states. This is because the CAR never binds for the bank in the good state.
  25
     Since we are assuming the contract cannot be state contingent, we must also assume that capital
regulations speci…c to the state are not observable or veri…able to the courts immediately at the begin-
ning of period 1. This would be the case if the relaxation of the constraint in the bad state were only
observed informally in the immediate aftermath of the shock; in e¤ect with the authorities con…rming
the relaxation only after some delay.



                                                  21
3.5    Recap: Key ingredients
Having discussed the results, it seems helpful to summarise the key determinants of
these results.

  1. Asymmetric information about the …rm’ residual assets. This ensures
                                                     s
     that credit lines increase surplus in the good state. By signing a credit line, the
     …rm enables the bank to observe its quality and to send a positive signal to the
     market about its quality. This means the market will more readily lend to the
     …rm in the good state. Without this signalling in the good state, the bank would
     have no incentive to o¤er more credit lines than its balance sheet could support,
                                                     s
     unconstrained, in the good state. The bank’ optimal exposure to credit lines
     would not then result in misallocation in the bad state.

  2. Shock to market’ ability to extract value from …rm’ residual assets:
                          s                                       s
     e.g. shock to liquidity of secondary markets. A su¢ ciently large shock in the
     bad state ensures that drawdowns in the bad state are high relative to available
     capital, and relative to drawdowns in the good state. This causes the regulatory
     constraint to bind in the bad state.

  3. Type 2 …rms are bank-dependent: e.g. their project payo¤s are unobservable
     to market lenders. This ensures heterogeneity across types of borrower, such that
     not all borrowers can or will hold credit lines with a bank. Since they are bank-
     dependent, the bank does not need to provide them with credit lines, in order to
     compete for their custom.

  4. The bank can still extract value from the residual assets of bank de-
     pendent …rms, despite problems in extracting value from credit line
     holders’residual assets. This ensures the marginal bene…t of lending to non-
     credit line holders does not decrease 1:1 with the increase in drawdowns: otherwise
     the unconstrained supply of loans to non-line borrowers will be su¢ ciently low such
     that the regulatory capital constraint does not bind in the bad state, despite high
     drawdowns.

  5. The state is non-veri…able. As a result, the bank cannot make the credit line
     contract state-contingent.
      These …ve points above are the key ingredients in this paper. However, using
      this discussion, we can generalize the framework; any model with the following
      characteristics will generate the same misallocation result:

  1. Credit lines must increase surplus in the good state:

  2. In the bad state, drawdowns must be su¢ ciently high relative to avail-
     able capital, such that the bank faces a regulatory constraint:

  3. Some …rms are unable (or choose not) to obtain credit lines:



                                          22
    4. The marginal bene…t of lending to non-credit line holders must not
       decrease 1:1 with the increase in drawdowns:

    5. The bank cannot make the contract state-contingent.


4       Empirical Methodology
Previous empirical research has examined the liquidity e¤ect of credit line drawdowns
(see Gatev et al. (2009), Gatev and Strahan (2006) Cornett et al. (2010), Ivashina and
Scharfstein (2009)). However, I argue that an extra e¤ect is present in the ratio of credit
lines to available regulatory capital. My theoretical model suggests that banks with
greater undrawn lines relative to regulatory capital will face greater constraints in issuing
new credit following a shock. This would show up as a nonlinear e¤ect in a standard
regression: an interaction between undrawn lines and the inverse of tier 1 capital. In
particular, this e¤ect would be pronounced following a severe shock to markets.
    I therefore construct a cross sectional dataset of bank balance sheet data, using the
collapse of Lehman Brothers as the shock. Previous work, such as Ivashina and Scharf-
stein (2009), documents anecdotal evidence that many corporates drew down on existing
credit lines following the collapse of Lehman. I examine the e¤ect of banks’exposure
to undrawn credit lines on their credit growth following the shock. In particular, I
show that the ratio of undrawn lines to regulatory capital is statistically signi…cant and
negative in a regression of credit growth.
    At this stage, this is suggestive evidence which is consistent with my theory. How-
ever, I cannot say much about causality, since I cannot properly control for selection
issues, as discussed below.

4.1       Call Report data
I use quarterly bank level data from Federal Reserve Reports of Income and Condition
(Call Reports) to construct a cross-sectional dataset26 . Each observation is reported at
the end of the quarter; so assets for quarter 4 of a given year re‡  ects the amount of
assets held by the bank going into quarter 1 of the following year.
    Following standard practice in empirical banking research, I have aggregated at the
high holder (HH) level so that each bank-quarter observation re‡ ects aggregate informa-
tion for a banking group. For the purposes of Call Report data, this means aggregating
by the identi…er rssd9348.

4.1.1      Data on credit lines
In addition to ‘                                                           o¤
                  balance sheet’ data, the Call Reports give data on ‘ balance sheet’
items. This includes undrawn credit lines. This is broken down into certain types of
credit line: e.g. there is an entry for total credit lines, and also one for credit lines with
maturity greater than 1 year. (This is relevant since the capital treatment of lines with
 26
      Data is available on the website of the Chicago Federal Reserve.



                                                   23
maturity less than 1 year is looser than for those with greater maturity; I explore this
in a later section).
    There is no data on drawn credit lines. In fact, capturing new loan growth is
complicated by the fact that total loans for a given quarter include newly originated-
and-drawn loans, as well as drawn credit lines. Given I want to explore the e¤ect of
credit line exposure on newly originated loans, I need to exclude the e¤ect of drawn
credit lines on new credit. Cornett et al. (2010) have a nice way of doing this. They
sum total loans and total undrawn lines for a given quarter, and de…ne this new variable
as ’        .
    Credit’ Taking di¤erences, this gives us:
                 Creditt =   (Total Loans)t +    (Total Undrawn Lines)t
    Any increase in total loans due to drawdowns of lines will be o¤set by a decrease in
total undrawn lines. To see this, suppose that there were no newly originated loans or
credit lines: an increase in total loans from t 1 to t came entirely from drawn lines. In
this case the positive term (Total Loans)t will be exactly o¤set by the negative term
  (Total Undrawn Lines)t . Of course, if there were no newly originated-and-drawn
loans, but the bank originated new, but undrawn, credit lines, this would show up as a
positive value for Creditt . The growth in credit variable, therefore, captures newly
originated supply of credit, whether drawn or undrawn. The key is that it does not
include credit that is associated with loans originated before period t.

4.2    Constructing variables
My key explanatory variable is exposure to credit lines, relative to regulatory capital.
I therefore take the ratio of total undrawn lines to tier 1 regulatory capital. In the
following tables, this variable is denoted as undrawn lines .
                                                 capital
    The timing of the shock lies towards the end of 2008 (although markets were increas-
ingly disrupted throughout that whole quarter). I construct a variable ‘ credit growth’
which re‡ ects the growth in credit from 2008 quarter 2 to 2009 quarter 4.
                                           credit09q4 credit08q2
                         credit growth =
                                                 credit08q2
As discussed above, the variable ‘credit’is de…ned as in Cornett et al. (2010).
    I am interested in banks’positions going into the shock. In order to avoid outliers,
I take averages of each independent variable for the three quarters preceding the shock.
For instance, ‘total undrawn lines’is calculated as

                       1                            X     2
  total undrawn lines’= (‘
  ‘                      total undrawn lines07q4 ’+     total undrawn lines08qi ’
                                                        ‘                       )
                       3                            i=1

   It is common in empirical banking research to normalize variables by assets. Previous
                                s
work has indicated that a bank’ size a¤ects its supply of credit; weighting by assets is
therefore designed to help compare banks on an equal footing (see Kashyap and Stein
(1997)). Moreover, when the dependent variable is a growth variable, it makes sense to
normalize independent variables by size to create similar units.


                                            24
    However, this is not an appropriate weighting for this paper. I intend to explore
whether the interaction term undrawn lines is signi…cant, over and above simply the level
                                           capital
of total undrawn lines. Yet, if I normalize all ‘         level’ variables by assets, I will end
up with two independent variables which are virtually indistinguishable undrawn lines and
                                                                                    capital
undrawn lines
    assets
              ; this is because capital and assets are highly correlated (approx 0.96 correla-
tion).27
    Instead, I correct for size in the following ways. First: I split the banks into quintiles
based on size (using assets as a measure of size). For each quintile, I compute the mean
asset level in the …nal quarters leading up to the shock. For each bank I then normalize its
independent variables by the mean asset level for the quintile in which it resides. This
has the bene…t of reducing the correlation between the normalized level of undrawn
lines and the exposure relative to capital.. My two variables of interest are therefore
undrawn lines         undrawn lines
   capital
               and av. group assets . The former will be labelled as ‘norm. tot. undrawn lines’
                                undrawn lines
and the latter simply as capital . Second, I normalize variables by each bank’ liquid       s
assets. Similar results are obtained from this robustness check.
    In the next part of this empirical section, I split banks into quintiles, based on their
relative exposure undrawn lines . I then run individual bank level regressions on a dummy
                          capital
for each group, controlling for other variables. The coe¢ cient on the dummy variable for
each group gives us the average or expected credit growth for that group, conditional on
controlling for other variables. I show that this coe¢ cient is signi…cant and decreasing
as we consider groups with higher exposure.
    Finally, I discuss ways to partially control for selection biases driven by demand
e¤ects in the data.


5       Empirical Results

Please see the appendix for summary statistics.

5.1     Nonlinear e¤ects
5.1.1    Normalizing by asset size, per quintile
In the following, I test whether the ratio of undrawn lines, relative to regulatory capital, is
signi…cant in a regression of credit growth. The theory implies that, due to the presence
of low capital charges on lines that are undrawn, a bank with high exposure to such lines
will face tighter equity capital constraints following a signi…cant amount of drawdowns.
This implies that the following interaction term should be signi…cant in a regression of
credit growth: undrawn lines
                    capital
    As we can see from Table 1, this nonlinear e¤ect is negative and signi…cant at the
1% level, controlling for the level of total undrawn lines and the level of capital.
  27                                   total undrawn lines
   It would not make sense to divide          capital        by assets; this variable is already e¤ectively
normalized’
‘          .




                                                  25
                                Table 1 Regressions: Whole Dataset
                                                           (1)
                               VARIABLES              credit growth

                               norm. undrawn lines        -0.0101*
                                                         (0.00535)
                               undrawn lines/capital    -0.0193***
                                                         (0.00362)
                               norm. capital               0.170**
                                                          (0.0850)
                               Constant                 0.0264***
                                                          (0.0102)

                               Observations                3,812
                               R-squared                   0.023
                               Robust standard errors in parentheses
                                  *** p<0.01, ** p<0.05, * p<0.1

  Normalized variables: each variable is divided by the average asset level for the size
                          quintile in which the bank resides.

   In Table 2, we can see the interaction term is still signi…cant when controlling for
quadratic terms in capital and undrawn lines, as well as the inverse of capital.

                               Table 2 Regressions: Whole Dataset
                                    (1)             (2)           (3)         (4)
       VARIABLES               credit growth credit growth credit growth credit growth

       norm. undrawn lines         -0.0101*      -0.00905*        -0.0148   -0.00712**
                                  (0.00535)      (0.00478)       (0.0110)    (0.00307)
       undrawn lines/capital     -0.0193***     -0.0201***     -0.0205***   -0.0197***
                                  (0.00362)      (0.00355)      (0.00355)    (0.00318)
       norm. capital               0.170**          0.194*         0.125     0.225***
                                   (0.0850)        (0.104)       (0.0908)     (0.0797)
       norm. liquid assets                         -0.0165        -0.0212
                                                  (0.0284)       (0.0312)
       norm. assets                                              0.00941
                                                                 (0.0132)
       norm. capital2                                                           -0***
                                                                                 (0)
       norm. inverse capital                                                1.906e+06**
                                                                              (965,247)
       Constant                  0.0264***      0.0283***       0.0281***      0.0187*
                                  (0.0102)      (0.00942)       (0.00919)     (0.00955)

       Observations                3,812          3,812           3,812        3,812
       R-squared                   0.023          0.024           0.024        0.028
                               Robust standard errors in parentheses
                                 *** p<0.01, ** p<0.05, * p<0.1
  Normalized variables: each variable is divided by the average asset level for the size
                          quintile in which the bank resides



                                                26
                                                  Table 3 Correlations
                          norm.      undrawn lines/ norm.       norm.             norm.          norm.
                       undrawn lines    capital      capital    assets         core deposits liquid assets
 norm. undrawn lines        1
 undrawn lines/capital   0.408             1
 norm. capital           0.950          0.332           1
 norm. assets            0.984          0.381       0.980         1
 norm. core deposits     0.732          0.216       0.882      0.804                  1
 norm. liquid assets     0.930          0.279       0.947      0.950               0.789           1
   p < 0:05,   p < 0:01,   p < 0:001


    As we can see from the correlations table, many of the variables exhibit high degrees
of correlation with one another. Such multicollinearity helps to explain why, when
we introduce more controls into the regressions in Table 2, we seem to …nd spurious
insigni…cance. For instance, in column 3, capital becomes insigni…cant when we also
control for (total) assets and liquid assets. Moreover, the level of undrawn lines becomes
insigni…cant in some of these regressions. Indeed, this e¤ect is not unique to regressions
including our variable of interest undrawn lines . If we drop this variable, the same e¤ect
                                        capital
occurs; as we can see in Table 4.

                                   Table 4 Regressions: Whole Dataset
                                               (1)            (2)          (3)
                  VARIABLES               credit growth credit growth credit growth

                  norm. undrawn lines      -0.00140**      -0.0190*         -0.0109
                                           (0.000564)      (0.0109)        (0.0121)
                  norm. assets                              0.00540        0.00615
                                                           (0.0131)        (0.0144)
                  norm. capital                              0.176*         -0.0889
                                                            (0.101)         (0.124)
                  norm. liquid assets                                        0.0130
                                                                           (0.0329)
                  norm. core deposits                                     0.0364**
                                                                           (0.0173)
                  Constant                 0.0159***        -0.00238       -0.00485
                                           (0.00265)       (0.00671)      (0.00745)

                  Observations               3,812           3,812         3,812
                  R-squared                  0.001           0.011         0.015
                                  Robust standard errors in parentheses
                                    *** p<0.01, ** p<0.05, * p<0.1
  Normalized variables: each variable is divided by the average asset level for the size
                          quintile in which the bank resides

    It is worth considering what we can ascertain from the more parsimonious regressions
in Tables 1 and 2. Clearly, by omitting causal variables such as assets, deposits, and
liquid liabilities this will produce omitted variable bias in the coe¢ cients. However, this
bias should be positive: which suggests the ‘  true’coe¢ cients on undrawn lines and their
interaction with capital are even more negative than those we observe. This supports


                                                   27
the case that high exposure relative to capital is associated with lower credit growth. (I
discuss other problems with bias from omitted demand e¤ects under the section titled
Futher work/Robustness Checks).

5.1.2   Results by bank size
When we split the dataset into groups, based on size, we can see the results discussed
above are driven by large banks. In the tables below, we de…ne a large bank as one
which is amongst the largest 40% of banks in the complete dataset.
   Table 5 shows that the nonlinear e¤ect is signi…cant for large bank:
                                        Table 5 Regressions: Large banks
                                           (1)             (2)           (3)         (4)
              VARIABLES               credit growth credit growth credit growth credit growth

              norm. undrawn lines         -0.0151*       -0.00450       -0.00926     -0.00686
                                         (0.00827)      (0.00436)      (0.00647)    (0.00419)
              undrawn lines/capital     -0.0180***     -0.0178***     -0.0160***   -0.0192***
                                         (0.00402)      (0.00376)      (0.00423)    (0.00411)
              norm. capital               0.0865*        0.245**          0.153       0.219*
                                          (0.0514)        (0.111)        (0.104)      (0.114)
              norm. liquid assets       -0.0836***     -0.0703***
                                          (0.0250)       (0.0231)
              norm. assets                0.0197*
                                          (0.0106)
              norm. capital2                                                           -0**
                                                                                        (0)
              norm. inverse capital                                                 3.491e+07
                                                                                   (9.420e+07)
              Constant                    0.0147        0.0155          0.0110       0.00970
                                        (0.00938)      (0.00947)       (0.0112)      (0.0106)

              Observations                1,524          1,524           1,524        1,524
              R-squared                   0.034          0.029           0.022        0.029
                                      Robust standard errors in parentheses
                                        *** p<0.01, ** p<0.05, * p<0.1
  Normalized variables: each variable is divided by the average asset level for the size
                          quintile in which the bank resides

   Table 6, however, shows the e¤ect is no longer present for small banks.




                                                      28
                                            Table 6 Regressions: Small banks
                                               (1)             (2)           (3)         (4)
                 VARIABLES                credit growth credit growth credit growth credit growth

                 norm. undrawn lines           -0.112         -0.213         -0.246       -0.279
                                              (0.198)        (0.202)        (0.196)      (0.187)
                 undrawn lines/capital       0.00199        0.00697        0.00693       0.0108
                                             (0.0200)       (0.0203)       (0.0200)     (0.0194)
                 norm. capital                  0.198        0.0999           0.224     0.320**
                                              (0.199)        (0.191)        (0.168)      (0.163)
                 norm. liquid assets        0.0831***       0.0687**
                                             (0.0292)       (0.0292)
                 norm. assets               -0.0441**
                                             (0.0220)
                 norm. capital2                                                         -3.21e-10
                                                                                       (5.75e-10)
                 norm. inverse capital                                                   565,156
                                                                                      (1.107e+06)
                 Constant                    0.0433*         0.0176         0.0247       0.0146
                                             (0.0231)       (0.0194)       (0.0191)     (0.0195)

                 Observations                 2,288          2,288           2,288          2,288
                 R-squared                    0.012          0.010           0.007          0.008
                                          Robust standard errors in parentheses
                                            *** p<0.01, ** p<0.05, * p<0.1
 Normalized variables: each variable is divided by the average asset level for the size
                         quintile in which the bank resides



5.1.3     Normalizing by liquid assets
As we can see in Table 7, qualitatively similar results are obtained if we normalize
variables by liquid assets, rather than by average assets per quintile.

                                        Table 7 Regressions: whole dataset
                                              (1)            (2)           (3)          (4)
        VARIABLES                        credit growth credit growth credit growth credit growth

        undrawn lines/liq. assets         -0.0151***          -0.0121*           -0.00359          0.000570
                                           (0.00412)         (0.00667)          (0.00612)         (0.00688)
        undrawn lines/capital              -0.00797*        -0.00999**         -0.0122***        -0.0127***
                                           (0.00432)         (0.00424)          (0.00379)         (0.00377)
        capital/liq. assets                                   -0.00499            0.0205            0.0143
                                                              (0.0154)           (0.0147)          (0.0130)
        assets/liq. assets                                                     -0.00451**       -0.00807***
                                                                                (0.00179)         (0.00284)
        credit growth                                                                            0.00707**
                                                                                                  (0.00292)
        Constant                           0.0404***         0.0435***         0.0534***          0.0492***
                                           (0.00457)         (0.00934)         (0.00654)          (0.00611)

        Observations                        3,812           3,812           3,812                   3,812
        R-squared                           0.027           0.027           0.031                   0.035
                                       Robust standard errors in parentheses
                                         *** p<0.01, ** p<0.05, * p<0.1


                                                          29
5.2    Using quintiles of exposure
In this section, I group the banks by the degree of their credit line/capital exposure.
Splitting the dataset into quintiles on the basis of undrawn lines , we can see that the mean
                                                        capital
credit growth of each group monotonically decreases as we consider groups with higher
exposure. In Table 8 below, I report the results of regressions of individual bank credit
growth on dummies for exposure quintile.

                             Table 8 Regressions with quintiles
                                                          (1)
                           VARIABLES                credit growth

                           group 2                      -0.00959
                                                       (0.00817)
                           group 3                    -0.0313***
                                                       (0.00825)
                           group 4                    -0.0445***
                                                       (0.00821)
                           group 5                    -0.0651***
                                                       (0.00866)
                           Constant                    0.0457***
                                                       (0.00590)

                           Observations                  3,812
                           R-squared                     0.021
                           F test: constant=group 2      33620
                           Prob > F                        0
                           F test: group 2=group 3        4501
                           Prob > F                        0
                           F test: group 3=group 4        4165
                           Prob > F                        0
                           F test: group 4=group 5        3739
                           Prob > F                        0
                            Robust standard errors in parentheses
   The dummy variable splits the banks into quintiles based on the variable undrawn
   lines/capital. This re‡ects exposure to undrawn lines, relative to available capital.
            Group 1 is the least exposed group: group 5 is the most exposed.

    The coe¢ cients are signi…cant for banks in the three more exposed groups. The
F statistics also show these coe¢ cients are monotonically decreasing. Note that the
coe¢ cient on group 2 is insigni…cant largely because it is so close to zero; this is not
necessarily inconsistent with the result that group means are monotonically decreasing.
Indeed, if we exclude the dummy for group 5 rather than group 1, the coe¢ cients on all
groups are signi…cant. Even when we control for other variables, these coe¢ cients are
signi…cant and monotonically decreasing (see Table 9).




                                             30
                               Table 9: Regressions with quintiles
                                   (1)            (2)              (3)       (4)
        VARIABLES             credit growth credit growth credit growth credit growth

        group 2                  -0.00956        -0.00961       -0.00615      -0.0140
                                (0.00817)       (0.00819)      (0.00843)    (0.00870)
        group 3                -0.0312***      -0.0313***     -0.0255***   -0.0362***
                                (0.00825)       (0.00829)      (0.00893)    (0.00951)
        group 4                -0.0445***      -0.0446***     -0.0371***   -0.0483***
                                (0.00821)       (0.00827)      (0.00927)    (0.00979)
        group 5                -0.0644***      -0.0651***     -0.0560***   -0.0667***
                                (0.00862)       (0.00870)       (0.0103)     (0.0101)
        norm. capital                           -0.000650        0.151*       -0.255*
                                                 (0.0203)       (0.0840)      (0.131)
        norm. assets                                                         0.00869
                                                                            (0.00724)
        norm. liquid assets                                                   -0.0207
                                                                             (0.0273)
        norm. core deposits                                                 0.0504***
                                                                             (0.0151)
        norm. undrawn lines     -0.00103*                     -0.0108**
                               (0.000611)                     (0.00515)
        Constant               0.0457***       0.0458***      0.0286**     0.0374***
                                (0.00590)      (0.00638)       (0.0114)     (0.0101)

        Observations             3,812           3,812           3,812       3,812
        R-squared                0.021           0.021           0.026       0.031
                              Robust standard errors in parentheses
                                *** p<0.01, ** p<0.05, * p<0.1
  The dummy variable splits the banks into quintiles based on the variable undrawn
  lines/capital. This re‡ects exposure to undrawn lines, relative to available capital.
           Group 1 is the least exposed group: group 5 is the most exposed.

   This lends further support to the hypothesis that high credit line exposure relative to
capital is associated with lower bank credit supply following a negative shock to credit
markets.

5.3    Future work/Robustness checks
In the above regressions, we cannot say anything concrete about causality. It could be,
for instance, that banks with high relative exposure are also the banks who faced lower
demand for credit following the Lehman collapse. Whilst this does not seem particularly
plausible, it is important to try to control for such demand e¤ects. Following Cornett
et al. (2010), I use the following variables to control for demand variation across banks;
                                                                                     s
the amount of commercial and industrial loans, and real estate loans, in the bank’ loan
portfolio. In Table 10 below, I show results where these variables are normalized by
group assets, as above, and also where they are calculated as proportions of the bank’   s
loan portfolio. The level of undrawn lines becomes insigni…cant in the latter regressions,
but the ratio of undrawn lines to capital remains signi…cant.


                                               31
               Table 10: Controlling for Demand E¤ects: C and I loans and Real estate
                                       (1)          (2)            (3)             (4)
           VARIABLES             credit growth credit growth credit growth credit growth

           norm. undrawn lines        -0.0213***      -0.0287**       -0.00824      -0.0128
                                       (0.00690)       (0.0115)      (0.00546)    (0.00941)
           undrawn lines/capital      -0.0193***     -0.0190***     -0.0181***   -0.0209***
                                       (0.00381)      (0.00382)      (0.00374)    (0.00339)
           norm. capital               0.331***       0.510***          0.136        0.110*
                                         (0.112)        (0.110)       (0.0869)     (0.0657)
           norm. C and I                0.119**         0.0456
                                        (0.0596)       (0.0523)
           norm. real est.            -0.0545***     -0.0786***
                                        (0.0154)       (0.0151)
           norm. liquid assets                        -0.0801**                  -0.0618**
                                                       (0.0337)                   (0.0275)
           norm. assets                                 0.0194                     0.0135
                                                       (0.0138)                   (0.0110)
           C and I / tot. loans                                      -0.108**    -0.127***
                                                                     (0.0433)     (0.0418)
           Real Est. / tot. loans                                   -0.158***    -0.178***
                                                                     (0.0208)     (0.0204)
           Constant                   0.0249***      0.0244**       0.152***      0.175***
                                      (0.00904)      (0.00992)       (0.0213)     (0.0188)

           Observations                 3,812          3,812           3,812       3,812
           R-squared                    0.032          0.036           0.043       0.047
                                    Robust standard errors in parentheses
                                      *** p<0.01, ** p<0.05, * p<0.1
    Normalized variables: each variable is divided by the average asset level for the size
                            quintile in which the bank resides

    However, this is still a fairly crude and imperfect control for demand variation, since
we cannot directly observe the demand side of loans in this dataset. As further work,
I intend to follow Ivashina and Scharfstein (2009) and use the Dealscan dataset, in
which we can observe the demand side of loan originations. However, this also presents
limitations since it does not cover demand across all types of borrower, only those within
the syndicated loan market. I am therefore also exploring the possibility of using a
richer dataset, in which both demand and supply can be observed for the full population
of banks and borrowers. Furthermore, …rm level data may enable me to more fully
disentangle the degree to which a reduction in credit growth represents misallocation of
credit across borrowers.


6      Conclusion
The key contribution of this paper has been to highlight the way capital charges on credit
lines can cause misallocation of bank credit following a market shock. Since undrawn
lines face much lower capital charges than drawn lines, the bank will face a sudden
increase in capital requirements when a large amount of credit is drawn from existing
committed lines. If regulatory capital is scare, the bank may have to cut back on lending


                                                    32
to other borrowers - those to whom it did not have a pre-commitment to lend. This
can result in misallocation of bank credit across di¤erent types of borrowers, despite
the bank setting optimal credit line exposure ex ante. Empirical evidence is at least
consistent with such an e¤ect.
    The drivers of this mechanism have been explored in the theoretical section. The
bank has an incentive to o¤er a large amount of credit lines. Credit lines produce
surplus in the good state by signalling …rm quality to the market, but are not associated
with any cost to the bank in the good state as long as they remain undrawn. By
relying on credit lines to provide a signal of …rm quality in the good state, the bank
will always have an incentive to set optimal exposure such that misallocation of credit
occurs in the bad state. This is accentuated if banks place low probability on the bad
state. Conversely, if there were no requirement for signalling at period 1, there would
be no need for credit lines and no ex post misallocation.
    This has implications for policy. Such misallocation is made worse if banks expect the
policy rate to be low in the good state. A low interest rate in the good state increases
the surplus obtained by credit lines in the good state. Anticipated interest rates in the
good state, rather than the bad state, therefore play a key role in a¤ecting the degree
of misallocation following market shocks. Regarding capital regulation, an increase
in the percentage capital requirement for undrawn lines (and thus a decrease in the
extra percentage requirement when they are drawn down) can decrease misallocation;
this is because it forces the bank to incur the cost of credit lines in the good state.
Furthermore, the model predicts that lower capital requirements in the bad state will
reduce misallocation in that same state.
    In future research, I intend to incorporate this model into a dynamic framework. This
will enable me to draw further implications for both countercyclical capital regulations
and monetary policy. Complementing this, I am exploring the possibility of obtaining
a richer dataset, in which I would be able to observe both the demand and the supply
side of credit provision. I could then examine the extent of misallocation in more detail.
Moreover, this would open up further possibilities of research, in particular to consider
how exposure to credit lines a¤ects monetary policy transmission.




                                           33
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                                         35
7    Appendix: Summary Statistics
                                                Summary Statistics 1
                                mean    sd     min max         10th      90th
                                                            percentile percentile
   norm. undrawn lines      0.20 3.54          0.00 161.67     0.01      0.18
   undrawn lines/capital 1.28 1.05             0.00 20.06      0.36      2.32
   norm. assets             1.00 4.18          0.05 180.75     0.09       1.29
   norm. core deposits      0.61 0.83          0.01 41.02      0.04      0.95
   norm. liquid assets      0.21 0.57          0.00 23.96      0.01      0.39
   Observations             3812
Normalized variables: each variable is divided by the average asset level for the size
                        quintile in which the bank resides

                                                   Summary Statistics 2
                                 mean    sd       min max         10th      90th
                                                               percentile percentile
    undrawn lines/liq. assets    0.97   1.38      0.00 31.11      0.13       2.11
    undrawn lines/capital        1.28   1.05      0.00 20.06      0.36       2.32
    capital/liq. assets          0.68   0.78      0.07 33.77      0.26       1.22
    core deposits/liq. assets    4.38   3.72      0.03 110.48     1.80      7.54
    assets/liq. assets           7.26   6.85      1.02 185.80     2.59      13.22
    Observations                 3812

                                                Summary Statistics 3
                                mean    sd     min max         10th      90th
                                                            percentile percentile
   norm. undrawn lines      0.20 3.54          0.00 161.67     0.01      0.18
   undrawn lines/capital 1.28 1.05             0.00 20.06      0.36      2.32
   norm. capital            0.09 0.24          0.00 10.91      0.01       0.14
   norm. liquid assets      0.21 0.57          0.00 23.96      0.01      0.39
   norm. core deposits      0.61 0.83          0.01 41.02      0.04      0.95
   norm. assets             1.00 4.18          0.05 180.75     0.09       1.29
   C and I / tot. loans     0.15 0.09          0.00 0.75       0.06      0.26
   Real Est. / tot. loans 0.69 0.17            0.00 1.00       0.45       0.88
   norm. C and I            0.10 0.45          0.00 18.29      0.01       0.18
   norm. real est.          0.43 1.01          0.00 48.10      0.05      0.72
   Observations             3812
Normalized variables: each variable is divided by the average asset level for the size
                        quintile in which the bank resides




                                             36
8     Appendix: Credit Lines vs Bank Loans
In the text, I show the bank will optimally choose the marginal credit line such that
there is misallocation in the bad state. However, is there a   such that the bank would
want to issue standard bank loans (non committed) to type 1 …rms in the range         !
but credit lines to a lower range c ! ? This would involve choosing             and c . I
discuss this below, and show that in fact the bank would always want to issue credit
lines rather than bank loans to the full range c ! .
    Given      can vary, it is not immediately clear whether CAR will in the bad state.
However, we can determine there is no optimal        and c for which the CAR does not
bind in the bad state. Suppose it were not to bind; then the bank would just issue bank
loans to all …rms in the range ! ; however, this immediately contradicts the premise
that the CAR does not bind (given condition 4).
                                                                              s
    In equilibrium, therefore, the CAR must bind. In this case, the bank’ problem,
corresponding to the function ( 7), will be given as follows
                     Z                                    Z
     S1       (1 q)      [pR + (1 p)      iG ]d + (1 q)      [pR + (1 p)        iG ]d
                                                                             c
                  Z                                        Z   bd (   )
             +q           [pR + (1   p)   iB ]d        q                  [pR + (1   p)   iB ]d
                      c

The …rst term re‡  ects the surplus from bank loans, whilst the second term re‡      ects surplus
from credit lines, both in the good state. The third term re‡           ects the (social) surplus
from drawdowns in the bad state, whilst the …nal term captures the foregone loans to
type 2 …rms in the bad state. As before, bd ( ) is given by the binding CAR in the
bad state
                                                                !
                                    bd ( ) =       c+
                                                                k
                    Loans to the type 1 …rms are negative NPV in the bad state for any
lender, given non pledgeable assets (see condition 1). The bank will therefore choose
not to lend to the type 1 …rms to which it does not have a commitment, i.e. those type
1 …rms in the range       ! .
    The …rst order condition for c is exactly the same as that in the main text. The
…rst order condition for      is given by
                                     @S                               !
                                            =   (1 p)(            c     )>0
                                     @                                k
                                         !
                     since        c         < 0
                                         k
                              !
    To verify that        c   k
                                 < 0, consider the following: the optimal c is the same as
in the main text, and the CAR in the main text is given by
                                                              !
                                           c+     bd ( c ) =
                                                               k
    Rearranging, this gives us
                                            !
                                       c      =     [       bd ( c )]
                                            k
                                              < 0


                                                  37
   As a result, the optimal problem is identical to that in the text and the bank will set

                                            =

     Intuitively, by o¤ering bank loans, rather than credit lines, to …rms with high , the
surplus is unchanged in the good state, but worse in the bad state. This is because the
loan to these types is negative NPV to the bank in the bad state, due to low pledgability
  B . As a result, in the bad state the bank ends up rationing these …rms, instead of type
2 …rms with lower . In equilibrium, the bank will prefer to commit itself via a credit
line to all type 1 …rms, because the …rm is willing to pay a higher ex ante fee than the
expected cost to the bank of such a commitment.




                                           38

				
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