Preliminary Comments welcome

The Great Recession and Bank Lending to Small Businesses

Judit Montoriol-Garriga* and J. Christina Wang#

August 2010

Abstract: The anemic recovery in employment since the depth of this recession has been blamed in part on the unusually weak performance of small firms. A policy question that has garnered attention in recent quarters is whether this weakness is largely attributable to credit constraints. To help shed light on this issue, this study utilizes a large loan-level data set to examine if the price and non-price terms on small business loans have been tightened more than those on large loans since the onset of the recession. To discipline the empirical analysis, the paper first develops a simple model of bank loan pricing that derives both the interest rates on loans actually made and the marginal conditions for loans that would be rationed. The empirical estimations then reveal that, once we account for the contractual features of business loans made under formal commitments to lend, there is at best limited evidence that either the price or the non-price terms on small business loans have experienced greater tightening during the Great Recession. This finding suggests that policy measures aimed narrowly to subsize lending to small businesses may not be effective in stimulating job growth.

JEL Classifications:

*: Supervision and Regulation Department, Federal Reserve Bank of Boston; Judit.Montorio-Garriga@bos.frb.org. #: Research Department, Federal Reserve Bank of Boston; christina.wang@bos.frb.org. We would like to thank Brent Bundick, Burcu Duygan-Bump, Patrick DeFontnouvelle, Jeff Fuhrer, Giovanni Olivei, Eric Rosengren, Geoff Tootell, Bob Triest and Vladimir Yankov for helpful comments. Many thanks to Chris Glynn and Vladimir Yankov for able research assistance. The views expressed in this paper are solely those of the authors and do not necessarily reflect official positions of the Federal Reserve Bank of Boston or the Federal Reserve System.

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I. Introduction

The U.S. recession that began in December 2007 has been dubbed the Great

Recession for its severity. Compared with all the previous post-war downturns, losses in

output and employment have been the steepest while the duration has been the longest

even if the NBER committee eventually decides to date it as ending in the second quarter

of 2009. Despite the depth of the slump, however, the recovery since then has been

disappointingly anemic, especially in terms of the lack of job growth that leaves the

nation’s unemployment rate hovering near its post-war high. Moreover, it has been noted

that small firms have experienced unusually deeper net job losses than large firms in this

recession, with much of the discrepancy attributed to the weaker birth rate of new firms.

It is therefore not surprising that one of the policy questions that have garnered

much attention since late 2009 as the U.S. economy started to emerge from the Great

Recession is why lending to small businesses has declined significantly in recent

quarters.1 To some, the lack of credit supply has become a primary suspect among

obstacles to the recovery of small businesses. Since small firms are deemed by many as

vital for job creation, credit supply to small businesses, or the lack thereof, has taken on

policy prominence as policy makers seek to stimulate employment growth in the

aftermath of the Great Recession. For instance, in his speech at the July 12th capstone

event for a series of more than 40 meetings aimed at addressing the financing needs of

small businesses, Federal Reserve Chairman Bernanke highlighted the contribution to

gross job creation by start-up enterprises and enumerated the various programs that the

Federal Reserve and other government agencies have initiated to facilitate credit flows to

small businesses.

It is however a difficult question what policy measures would be effective in

encouraging either expansions of existing businesses or creations of new ones. In

particular, one must ask to what extent the contraction in the amount of business debt

outstanding seen in this downturn is due to the lack of demand, as opposed to constraints

1 Total small commercial and industrial loans made by commercial banks declined 3.2% between 2008 and 2009, according to the June Call Reports.

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on credit supply. For instance, many bankers argue that the shrinking volume of small

business loans is more due to the lack of demand from creditworthy small firms as these

firms have had to cut production in the face of much weaker sales. If the reduction in

borrowing is demand-driven, then the focus should be conventional monetary plus fiscal

policy tools and, in the current zero-lower bound environment, unconventional monetary

stimuli should be considered as well.

On the other hand, if there ever was a downturn triggered by system-wide

financial shock in the U.S. since the Great Depression, this downturn is the foremost

candidate. Furthermore, capital constraints on financial institutions that suffered sizeable

subprime-mortgage-related losses have likely amplified the negative shock to the

economy from the bursting of the housing bubble. If the lack of credit is an important

impediment to the recovery, then policy response should include measures that encourage

lending. Regulatory and supervisory policy can play a useful role in this regard. For

instance, it is important for supervisors to know to what extent their concerns about bank

safety may have, inadvertently, constrained lending to small firms that are fundamentally

sound but experiencing cash flow shortfalls in the near term. If there is indeed truth in

this claim, then the remedy should in principle be straightforward: reduce such

supervisory constraints to the fullest extent feasible. In addition, banks should be

compelled to raise capital if current or expected capital shortfall is hindering the growth

of their loan portfolios.

To the extent that supply-side credit constraints have played a larger than usual

role in this downturn, small businesses likely have been more adversely affected than

large firms. A number of previous studies suggest that financial constraints are more

binding on small firms (see, e.g., Gertler and Gilchrist, 1994). For one thing, bank-

dependent firms are found to display more signs of being financially constrained (e.g.,

Kashyap et al., 1994), and small businesses depend almost exclusively on bank financing.

On the other hand, for this recession, some may contend that it is unclear that small firms

have encountered greater credit rating, since community banks, which are considered the

bulwark of banking relationship for small firms, were largely unscathed. This is,

however, no longer an accurate depiction of the pattern of small business lending in the

U.S. over the past decade or so. As many have documented, banks with more than $50

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billions in assets have steadily increased their share of small business loans since the mid

1990s and now account for over 50 percent of such loans. If small firms have indeed been

disadvantaged also in this downturn, then policies such as expanding government

guarantees on small business loans through programs run by the Small Business

Administration can prove effective in speeding up the recovery.

This study seeks to help answer the question whether, relative to large firms,

small firms saw worse deterioration in the cost and availability of credit during this

downturn. To this end, this paper first develops a model of bank loans to offer structural

guidance for the specification of loan yield and spread regressions. The model adapts the

costly state verification model to show how bank loan yields and spreads should depend

on a loan’s expected default loss and the lending bank’s opportunity cost of funds. It links

these quantities to loan attributes, such as a loan’s size and whether collateral is pledged.

It also suggests bank characteristics that are likely to affect a bank’s cost of funds.

Perhaps even more importantly, the model seeks to derive empirical implications for

detecting credit rationing. Specifically, what patterns in realized loans (and thus

observable to the econometrician) are most suggestive of the presence of rationing?

The paper then uses a loan-level dataset to explore the dynamics of small business

lending during the Great Recession. To exploit the strength of the data, we focus on

investigating if small firms have experienced more severe tightening in both the price and

non-price dimensions of loan terms such as maturity and collateral requirement. We also

examine to what extent bank-level factors (such as capital and liquidity adequacy) that

have been found to influence a bank’s willingness to supply credit have affected both the

volume and terms of its small business loan origination. We then explore regressions that

should help better detect signs of credit rationing according to the model’s derivations.

Our empirical analysis confirms that small loans on average pay higher interest

rates, have shorter maturities and more likely to pledge collateral, as found in previous

studies. However, our analysis also uncovers hitherto largely neglected features of the

data that can overturn the conclusion regarding the relative change in terms on small

loans during the Great Recession. Specifically, we find that the estimation results are

sensitive to how loans made under existing commitments are treated. Compared with the

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new term loans, these commitment-based loans have two institutional features that pose

problems for the specification of the yield and spread regressions. First, for most of these

loans, the spread over a base rate is fixed at the level set in the commitment contract, and

thus pre-determined with respect to the loan contract itself. Second, multiple base rates

are used in commitment contracts, and the base rate is almost invariably allowed to float

with the market. Once we take into account these features of loans made under existing

commitments, we find little evidence that the interest rates on small business loans rose

more than on large loans during this downturn. In addition, small business loans did not

see their maturity shortened more than large ones, and nor were they any more likely to

be required to pledge collateral during this recession.

The remainder of the paper is organized as follows. Section II presents the model

that derives both the conditions for observed interest rates on loans actually made, and the

likely manifestation of credit rationing by banks. It also discusses briefly what the model

implies about empirical specifications. Section III then conducts the empirical analysis,

focusing on the relative change in loan terms for small loans relative to large ones. It then

discusses policy implications of the empirical findings. Section IV concludes.

II. A Model of Bank Lending and the Distribution of Loan Interest Rates

This section develops a model of the optimization problem that banks solve in

setting the contractual interest rate to charge on each loan based on that borrower’s risk

profile as well as other relevant factors such as the aggregate state of the economy. This

model incorporates several features that have been adopted often to rationalize credit

rationing. Accordingly, it investigates how the business cycle may affect the types of

borrowers who receive credit and in turn the distribution of loan interest rates. In

particular, it explores the following questions: 1) what are the plausible reasons for

(increased) credit rationing during economic downturns, especially of small firms, and 2)

if more borrowers are indeed denied credit during bad times, how would it manifest in the

range of interest rates paid by those borrowers who in fact are granted credit?

As an extensive literature on financial intermediation has established, banks

facilitate credit supply by screening and monitoring borrowers to mitigate the asymmetric

information problem. For instance, Diamond (1984) shows that it is more efficient for

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suppliers of funds to delegate the monitoring function to banks, instead of duplicating one

another’s monitoring effort. Here we adapt the widely used “costly state verification”

model a la Townsend (1979) to characterize bank loan contracts. Specifically, a

borrower’s realized return or collateral value is assumed to be costlessly observable only

to herself, while anyone else must conduct costly monitoring to find out the true ex post

value. As Townsend (1979) and Gale and Hellwig (1985) have shown, in environments

of this kind, risky debt is the optimal contract for external financing. Then, at the maturity

of a loan, if the borrower does not repay the interest as set out in the contract, the lending

bank conducts the audit and receives all the residual payoff or liquidation value of

collateral, or both.2 As is customary to this class of models, the monitoring is assumed

perfect in that it is able to fully uncover the true return.

Since a key objective of the model is to study how aggregate fluctuations along

with heterogeneity in credit quality across borrowers affect the quantity and price of

credit, we follow Bernanke, Gertler and Gilchrist (BGG, 1999) in our modeling of the

return on each project as subject to both project-specific and aggregate shocks.

Specifically, we assume that, at the end of a period t, project i’s realized gross return

equals θiRt+1.3 θi represents the project-specific return prospect: we assume that there is a

continuum of potential projects indexed by the idiosyncratic return type θi. These are

i.i.d. random draws across projects as well as over time, with E(θ) = 1. We further

assume that θi’s follow a differentiable c.d.f. H(θ) over a non-negative and bounded

support. We will see that, had every loan identical terms, there would be a one-to-one

(inverse) mapping between θi and default probability. So θi can be construed as an

observable signal of a borrower’s default probability. In reality, θi can be either readily

observable to a bank, such as a borrower’s credit score nowadays, or the bank can choose

to screen an applicant to discern her type θi. Banks are assumed to possess the

2 The monitoring here does not alter the intrinsic risk profile of the projects that banks fund, keeping the model more tractable without loss of the key feature of bank lending for our purpose – potentially a higher cutoff level of borrower creditworthiness during economic downturns. See Diamond (1991) for a model of monitoring that mitigates the moral hazard problem by altering borrowers’ incentive and in turn risk-return profile of the project. 3 The subscript (t+1) signifies that the return is not realized until the end of period t.

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technology that enables them to accurately discern each applicant’s type.4 This

simplifying assumption enables us to consider only banks’ monitoring function as the

element that drives a time-varying wedge between internal and external funds.5

Each project’s exposure to aggregate risk is represented by Rt+1, which is the

common component of returns that will be realized on all projects funded at the

beginning of period t. Business cycle fluctuations influence loan approval and terms via

the time-t expected distribution of Rt+1. Denote the c.d.f. of this conditional distribution

Ft(Rt+1). We first illustrate the impact of time-varying expectations of Ft(Rt+1) with the

simplest case where it is degenerate at a single value Rt+1. Later we will consider the more

general case where Rt+1 is governed by two different distributions corresponding to

whether the overall economy will be in a high (boom) or a low (recession) state.

In addition to the aggregate return shock, each project is also subject to

idiosyncratic shocks denoted by ωi. So the overall realized return of project i at the end of

period t will equal , 1 1i t i tRω θ+ + . The ωi’s too are i.i.d. random draws across projects as well

as over time, with E(ω) = 1. We further assume that ωi’s follow a differentiable c.d.f.

G(ω) over a non-negative and bounded support. One way to characterize the distinction

between large and small firms without introducing heterogeneity along a second

dimension (i.e., project size) is to assume that small firms each has only one project

whereas large firms are simply a portfolio of projects. So, as a firm’s size increases,

idiosyncratic shocks accounts for an ever smaller share of its overall return volatility

owing to diversification, and its return converges to the average of project θ’s, which

equals 1. That is, the return process of large firms is mostly driven by aggregate risk

Rt+1.6 Under this formulation, small firms display greater volatility in returns because of

4 In addition to internal rating or standardized credit score, banks likely also rely on mechanisms such as offering prospective borrowers a menu of leverage and collateral ratios, similar to the mechanism studied in Leland and Pyle (1977). Unfortunately, available data do not allow us to condition on such information. 5 We ignore how banks’ costs incurred in the screening activity might affect loan terms. Such costs are often rolled into loan principal, and they should have little effect on default probability so long as they are small relative to the loan amount intended to fund the project. In fact, screening costs likely matter most for medium-small loans that are too big to be originated using standardized scoring software. 6 We recognize that we are ignoring systematic cross-industry differences in the magnitude of cyclical fluctuations. For instance, the auto industry is dominated by large firms, but it also faces above-average cyclical movements in demand. We ignore this heterogeneity because we do not observe individual loan’s industry affiliation in our data.

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their draws of idiosyncratic shocks, that is, var(ωR) = var(ω) + var(R) > var(R). As

Stiglitz and Weiss (1981) have shown, since a lender’s payoff is concave in a project’s

overall payoff, greater volatility in the form of mean-preserving spreads increases the

default probability for any given loan interest rate and will thus more likely result in

credit rationing.

2.1 Equilibrium Condition for Individual Loans

Now we examine how a bank determines whether to lend to a borrower of type θi

and what interest rate to charge, and how these decisions are influenced by the state of the

economy. Since the focus in this study is bank C&I loans, which tend to be short-term

with variable interest rates, we start with a model of loans as one-period debt contracts.

Later we will develop an extension to account for the fact that the majority of bank C&I

loans are made under an existing commitment, and the loan interest spread (over a time-

varying reference rate such as the prime rate) is generally pre-specified in the

commitment contract.

In each period t, individual borrower i is assumed to have one project with a pre-

determined scale, whose size is denoted as itK .7 The borrower may put up her own

wealth to finance part of the project and borrow the rest. However, since we do not

observe leverage, we omit this dimension of heterogeneity from the baseline model. We

will illustrate later that all the qualitative results of the model continue to hold in an

extension that accounts for differing leverage across borrowers. Denote i’s contractual

interest rate (also referred to as the yield to maturity) as , 1ˆ

i tZ + .8 Then i is deemed in

default if, at the end of period t, i’s overall return falls short of the required interest

payment, i.e., , 1 1 , 1ˆ

i t i t it i t itR K Z Kω θ+ + +< .9 So, for given θi and Rt+1, there is a one-to-one

7 Given that we do not observe any borrower characteristic in the data, this assumption is made for convenience, so that we avoid the need to derive an individual borrower’s optimal choice of Kit. More generally, this can be interpreted as representing cross-industry differentials in scale, which are largely driven by differences in production technology. 8 Even though , 1

ˆi tZ +

is contracted and thus known at the beginning of t, we keep the (t+1) subscript to signify its dependence on random returns ωi,t+1 and Rt+1, the realization of which determines whether , 1

ˆi tZ +

can be met. 9 We ignore technical default of loan covenants, primarily because we have no data on covenants.

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mapping between , 1ˆ

i tZ + and a threshold value of idiosyncratic return ωi,t+1 (denoted , 1ˆi tω + ;

note that it is known at time t), below which loan i is considered in default:

, 1 , 1 1ˆˆi t i t i tZ Rω θ+ + += . (1)

Note that , 1ˆ( )i tG ω + is the default probability. Clearly, the default probability rises

in the loan interest rate charged , 1ˆ

i tZ + , all else equal, because there is less chance that the

cash flow will be sufficient to cover the loan payment. Consistent with intuition, (1) also

shows that, for any given , 1ˆ

i tZ + , a higher value of θi lowers a borrower’s odds of default,

meaning that the partial effect of higher credit quality is a lower , 1ˆi tω + . In fact, if every

loan had identical terms, θi would be the sufficient statistic for default probability. By

comparison, a higher Rt+1 lowers default probability for all borrowers.

A borrower can pledge assets as collateral for the loan. Even though collateral

(absent its incentive effect here) does not alter the default probability of a loan, it lowers

the lender’s loss given default and hence raises her expected return on the loan. So, as

will be shown below, for borrowers whose applications would have been approved

without any collateral, pledging more collateral lowers the interest rate at the margin. On

the other hand, a more subtle effect of collateral is that it enables some borrowers of low

(unobserved) quality, who would otherwise be rationed out of the market, to obtain

credit. Since these marginal borrowers are the most risky, controlling for observed

signals of credit quality, the observed loan interest can in fact be positively correlated

with the incidence of collateral.

The value of collateral, or more precisely the lack thereof, may have played an

unusually big role in small business lending during the latest recession, which is chiefly

induced by the sizeable real estate price correction. According to the most recent survey

conducted by the NFIB, many small businesses use commercial real estate as collateral

for their borrowing, and many of these commercial properties have become seriously

“under water.”

For brevity of exposition, in all the ensuing analysis, we assume that the lender

cannot recover any of the actual project return if a borrower defaults. Instead, the lender

can recoup losses only by paying a monitoring-cum-liquidation cost to extract the value

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of the collateral. Assuming a constant partial recovery rate alters none of the model’s

qualitative results except adding complexity because then not only the default probability

but also loss given default would depend directly (and negatively) on a borrower’s type

θi. Here we also ignore the possible screening function served by collateral.

We now analyze how a bank should set the interest rate when lending to a type i

borrower. From the bank’s perspective, the interest rate charged must generate an

expected rate of return (net of the monitoring cost) no less than its risk-adjusted

opportunity cost of funds. The lending bank can charge a markup in accordance with its

market power. For simplicity, we assume that this markup takes the form of a constant

multiple over the bank’s ex ante cost of funds. Accordingly, in all the ensuing analysis,

the cost of funds can be interpreted as inclusive of the bank-specific markup.10 This is

one reason that a bank’s expected rate of return can deviate from that on market securities

with comparable risk characteristics.

If we explicitly consider collateral, then the contractual interest rate , 1ˆ

i tZ + , which

corresponds to the cutoff value for idiosyncratic returns , 1ˆi tω + , must satisfy:11

( ) , 1

, 1

ˆ

, 1 ˆ 0ˆ ( ) ( )i t

i ti t it it it t itZ K dG A M dG K

ω

ωω ω µ+

+

∞

+ + − =∫ ∫ . (2)

Ait denotes the collateral value to the lender; what matters for setting the loan interest rate

is how much the lender can expect to recoup via the collateral.12 So Ait may well be less

than what the collateral is worth to the borrower, if the lender does not have the necessary

technology to realize the full value of the collateral.13 Mit denotes the lender’s cost of

monitoring a defaulted borrower, including the cost incurred to liquidate the collateral. It

10 In reality, a bank is likely to vary the markup both across borrowers and over time. 11 To be precise, a lender should form expectations also regarding the state of the economy next period conditional on the state this period. This can be formalized by assuming a Markov transition matrix between the aggregate states. For now we ignore this layer of the expectation formation and will analyze it later. 12 This implies another subtle point: the lender should care about the expected value of the collateral when the loan matures at the end of the period, not its value today. This consideration is likely to matter the most when non-trivial change in the collateral value is expected over the duration of the loan, such as in the case of commercial real estate loans. Lenders typically take account of this by adjusting the upper bound of the loan-to-value (LTV) ratio: the greater the expected appreciation of the collateral value, the higher the LTV allowed, and vice versa. 13 For example, the secondary-market resale value of a piece of specialized equipment may fall far short of its shadow value as installed capital in a solvent firm (equivalent to Tobin’s q).

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can be time-, project- and bank-dependent, since it is a reduced-form representation of a

bank’s cost function for producing monitoring services. Here for brevity we omit the

bank-specific element from the subscript. Mit is the main element that drives a wedge

between internal and external funds for a firm.

µt is the ex ante (marginal) cost of funds for the bank (inclusive of the markup);

the bank subscript is omitted for convenience. The cost of funds should equal a weighted

average of the bank’s cost of debt and (shadow) cost of equity. If the lending bank itself

faced no additional frictions (due to information or agency problems) in raising external

funds, then the cost of funds for a loan should equal the rate on a market debt with the

same risk profile (primarily maturity and risk rating); otherwise arbitrage opportunities

would arise. However, we know from previous studies such as Froot and Stein (1998),

financial institutions themselves face frictions in raising external funds other than insured

deposits. In particular, a bank facing capital constraint can be thought of as having a

prohibitively high shadow cost of equity and most likely facing a higher cost of raising

debt as well.

Substituting (1) into (2) and rearranging terms, we can express (2) all in terms of

rate of return:14

( ) ( ), 1 , 1 1 , 1ˆ ˆ ˆ

i t i t i t i t it it tZ G Z R Z m aθ µ+ + + +− + − = . (3)

it it ita A K= and it it itm M K= are, respectively, the collateral and the monitoring

expense normalized by the size of the loan. Note that ait is the inverse of the so-called

loan-to-value ratio for secured loans.15 The first term is equivalent to the lender’s

expected return if the borrower had no default risk. This risk-free payoff is reduced by the

expected default cost, i.e., the second composite term. Should the borrower default, the

lender would lose all the contractual interest , 1ˆ

i tZ + (recall that we assume the lender

recovers none of the residual project payoff from a delinquent borrower), have to pay the

monitoring expense mit but, if the loan is secured, recoup the collateral’s worth ait. Note

14 This condition can be equivalently written as ( ) ( ) ( ), 1 , 1 1 , 1 1

ˆ ˆ ˆ1i t i t i t i t i t it it tZ G Z R G Z R m aθ θ µ+ + + + + − − − =

. The

first composite term is the lender’s expected payoff from the project, while the second term is the expected net cost due to default. 15 Also, 1–1/ait equals the so-called hair-cut or margin requirement in collateralized lending.

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that in this model, mit and ait have symmetric effects on , 1ˆ

i tZ + : any offsetting changes

would leave , 1ˆ

i tZ + unchanged.

For simplicity, we assume that the second composite term in (3) is always

negative, meaning that the lender on net expect to lose income on a delinquent borrower.

But we allow, in the case of secured loans, the expected collateral value to be sufficient to

cover the monitoring expense, or even just the contractual interest on the loan. That is,

0it itm a− < but , 1ˆ 0i t it itZ m a+ + − > . (4)

More generally, the lender’s payoff from a delinquent borrower equals

, 1ˆmin ,i t it itZ a m+ − , since it is possible that the full value of the collateral is more than

enough to make the lender whole should the loan not get repaid. However, casual

observation suggests that banks almost invariably prefer collecting interest to liquidating

the collateral of a delinquent borrower. So (4) seems a plausible simplifying assumption.

In short, equation (3) implicitly defines loan rate , 1ˆ

i tZ + as a function of θi, ait, mit,

Rt+1, µt and the distribution of idiosyncratic returns G(ω). In this formulation, there is a

one-to-one mapping between , 1ˆ

i tZ + and the expected default loss

( ) ( ), 1 , 1ˆˆi t i t it itG Z m aω + + + − , which is monotonically increasing in , 1

ˆi tZ + . If we interpret the

loan-level credit rating to be discrete ordinal labels for non-overlapping intervals of the

continuum of expected default losses, then there should be no overlapping loan yields

across rating classes. Within each rating class, loan yields should be a monotonic

transformation of the expected default losses. In actual data, however, loan yields overlap

across ratings, even within a bank. We will discuss the likely reasons in the empirical

section.

For the analysis here, we take the parameter mit in (3) to be the most distinct

between large and small loans. Anecdotal data suggest that there is a somewhat fixed

component of the monitoring cost, including the variety of fees (such as to accounting

and law firms) related to restructuring and liquidation, and the cost in general does not

rise proportionally to the size of the loan. Therefore, the monitoring cost per unit of loan

balance is most likely a concave function of loan size, meaning that the smaller a loan,

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the greater its unit monitoring cost mit. Everything else equal, this implies that the smaller

the loan, the higher the interest rate , 1ˆ

i tZ + , as will be shown below. Furthermore, this

renders small borrowers more susceptible to credit rationing and, under certain

conditions, especially during economic downturns.

2.2 Conditions for Credit Rationing and Possible Cyclical Patterns

A marginal increase in the loan rate , 1ˆ

i tZ + , and hence the threshold return , 1ˆi tω + ,

has two opposite effects on a lender’s return: on the one hand it raises the marginal return

by ( ), 1ˆ1 i tG ω + − through a higher non-default payoff but on the other hand it raises the

probability and hence the net cost of default by ( ) ( ), 1 , 1 1ˆ ˆit it i t i t i tm a Z g Rω θ+ + +− + . Given

assumption (4), there exists a cutoff level , 1i tZ + at which these two effects offset, with

, 1i tZ + solving

( ) ( ), 1 , 1 , 1 , 1i t i t i t i t it ith Z Z m aω ω+ + + += + − , (5)

where ( ) ( ) [1 ( )]h g Gω ω ω≡ − is the hazard rate. If we further assume that16

( ) 0hω ω ω∂ ∂ > , (6)

then , 1i tZ + is the unique interior solution that maximizes the lender’s expected return. For

any , 1 , 1ˆ

i t i tZ Z+ +< , the lender’s expected payoff increases with , 1ˆ

i tZ + , i.e.,

( ) ( ), 1 , 1 , 1 , 1ˆ ˆˆ ˆi t i t i t i t it ith Z Z m aω ω+ + + +< + − , and vice versa. So no lender would charge a

borrower beyond the maximal rate , 1i tZ + . Instead, they would refuse to lend to borrowers

whose required loan rate as determined by (3) exceeds the maximum. We can interpret

this situation as rationing – such borrowers are shut out of the credit market.

How , 1i tZ + changes with the borrower- and loan-specific attributes can be

examined by fully differentiating (6). We illustrate with the comparative static of , 1i tZ +

16 As shown in BGG (1999), this condition is satisfied by any monotonic transformation of the normal distribution.

13

with respect to θi:

( )( )

( ) ( ), 1 , 1, 12

, 1

i t it it i ti t i

ii t it it

Z m a Z h hdZ d

ZZ m a

ω ω ω ωω ω θω ω θ

+ ++

+

+ − − ∂ ∂ ∂ ∂ − =∂ ∂ ∂ ∂ + −

. (7)

By assumption (4), the first term in the square bracket on the left hand side is

negative.17 By assumption (6) and the relationship between ω and Z defined in (1), the

second term in the bracket is positive. For the same reason, the coefficient on the right

hand side is negative. With negative coefficients on both sides, we derive that

, 1 0i t idZ dθ+ > , that is, the cutoff loan rate is increasing in θi. This result conforms with

our intuition: all else equal, borrowers with higher credit quality are less likely to hit the

upper limit of loan rate and face rationing.

Since θi and the expected aggregate return Rt+1 have symmetric effects on , 1i tZ + ,

we can easily tell that , 1 1 0i t tdZ dR+ + > . Yet again, this is an intuitive result: more

optimistic expectations about the aggregate state of the economy lower the likelihood of

borrowers being rationed, ceteris paribus. It is readily shown with similar algebra that

, 1 0i t itdZ da+ > and , 1 0i t itdZ dm+ < . That is, more collateral or lower audit cost (both

relative to the loan size) enables a borrower to remain viable to a lender at higher interest

rates and thus less likely to face rationing.

Since , 1i tZ + is the highest feasible interest rate to charge, any difference in

parameter values across borrowers that would drive down , 1i tZ + so that it would be

exceeded by the necessary loan rate would need to be offset by changes in other

parameters to avoid rationing by banks.18 For instance, denote the marginal borrower J

and her vector of attributes as { , , }J J Jt JtX m aθ′ = , conditional on the expected aggregate

return Rt+1. By definition, we have , 1 , 1ˆ

J t J tZ Z+ += . If there exists another borrower j with a

17 Note, however, that this term turns positive if the collateral is insufficient to cover the monitoring cost, including when a loan is unsecured, i.e., ait = 0. Then it is possible that the coefficient on the left hand side becomes positive. For simplicity, we rule out this possibility. 18 As will be shown in the next section, changes in parameters (across borrowers or over time) that lower

, 1i tZ + generally also raises the necessary loan rate , 1ˆ

i tZ +, making it more likely that a borrower would

become ineligible for funding.

14

higher unit audit cost mjt, then in order for j to still be eligible for credit, she would need

to have a higher intrinsic credit quality θj, or put up more collateral ajt, or both. This is

perhaps a case particularly relevant for small loans, since they generally have high audit

cost relative to the size of their borrowing. This may well be a reason why, all else equal,

a bigger fraction (in terms of the range of θ ’s) of small borrowers may be rationed.

This upper bound on loan rate may not be reached for any borrowers within the

given range of values for θi, ait, mit and µt. This corresponds to a situation with no credit

rationing, in that all borrowers who want funding have their demand satisfied. Such an

outcome is more likely during good times, represented here by a high Rt+1. Since , 1i tZ +

rises in Rt+1, a bigger fraction of borrowers are likely to face credit rationing if

expectations of the overall health of the economy deteriorate. According to the

comparative statics above, the borrowers most likely to be rationed when times turn bad

are those already marginal – with worse return profile, less collateral or higher unit

monitoring cost (such as small borrowers), or a combination of all three. In other words,

the marginal borrower in recessions is likely to be of a better return type, with more

assets and larger. The more severe the downturn, the bigger the shift in the marginal

borrower’s attributes. This can be a reason to suspect that more borrowers, especially

small borrowers, are being rationed in this recession.

The element that may have played a bigger than usual role in curtailing credit

availability during this latest downturn is the loss of collateral value ait, as a result of the

slump in both residential and commercial real estate markets. This may be particularly

relevant for small businesses, among which the use of home equity and other real estate

as collateral is more prevalent. In addition, given the severity of this downturn, the

haircut borrowers would have to take on the accounts receivable as collateral almost

surely has been raised as well. As a result, the marginal borrower now must be of a higher

quality (i.e., higher θi), assuming no change in mit. This would lead to a larger fraction of

borrowers being rationed out of the bank loan market since the onset of this recession.

Yet another force that can also help drive up the intrinsic credit quality θi of the

marginal borrower in recessions is banks’ cost of funds µt. To the extent that a bank

raises funds at the margin from sources other than insured deposits, the risk premium it

15

faces on its funding rises during bad economic times. This would in turn require the bank

to raise the interest rates it charges on loans, since it is easy to see from (3) that

, 1ˆ

i t tR µ+∂ ∂ > 0. However, this may not be feasible for those marginal borrowers who

were already paying interest rates closest to maximal feasible rates during good times.

Since, as explained above, their ait and kit both tend to move also in the direction of

raising the required loan interest rate, it is no longer feasible for the bank to lend to these

previous near-marginal borrowers.

2.3 Interest Rates Paid by Funded Borrowers and the Cyclical Patterns

In terms of the interest rate charged on realized loans, equation (3) and condition

(6) imply the intuitive relationship that the better a project’s type, the lower the loan

interest rate , 1ˆ

i tZ + and hence the cutoff level , 1ˆi tω + . That is, , 1ˆ 0i t idZ dθ+ < , since

( ) ( )( ) ( ) ( )

, 1 , 1 , 1, 1

, 1 , 1 , 1 , 1 , 1

ˆˆ ˆ ˆˆ ˆˆ ˆ ˆ1 1

i t i t i t it it ii t

i i t i t i t i t it it i t

g Z m adZd G h Z m a Z

ω ω θ

θ ω ω ω+ + ++

+ + + + +

− + −=

− − + − . (8)

Condition (6) ensures that ( ) ( ), 1 , 1 , 1 , 1ˆ ˆˆ ˆi t i t i t i t it ith Z Z m aω ω+ + + +< + − when , 1 , 1

ˆi t i tZ Z+ +< and

so the denominator is positive, while assumption (4) means the numerator is negative.

Along with (1), result (8) implies that

( ) ( ), 1 , 1 , 1 , 1 , 1 , 1ˆ ˆˆ ˆ ˆ ˆ 0i t i i t i t i t i i t i i t id d Z dZ dω θ ω θ ω θ ω θ+ + + + + += ∂ ∂ + ∂ ∂ < ∂ ∂ < .

The intuition of this result is that projects of better types have lower default probability

G(ω) beyond the marginal effect of better intrinsic returns (i.e., ∂ω/∂θ < 0) because they

also enjoy lower interest rates.

Since Rt+1 and θi have symmetric effects on , 1ˆ

i tZ + , we know that , 1 1ˆ 0i t tdZ dR+ + < ,

meaning that loan interest rates tend to be lower during times of better expected

aggregate states of the economy. Similar algebra shows that , 1ˆ

i t itdZ da+ < 0, and

16

, 1ˆ

i t itdZ dm+ > 0.19 In words, loan interest rates need to be higher for borrowers with less

collateral or higher unit monitoring cost.

The bank’s cost of funds µt is assumed in (2) to be identical for every type of

borrower, although in reality it is more likely to be a decreasing function of observable

indicators of the borrower’s credit quality, i.e., θi in the context of this model. Research

on publicly traded corporate bonds finds considerable risk premia that rises (in absolute

level) for lower rated bonds (see, e.g., Berndt et al., 2005 and Elton et al. 2001), and risk

premia on low rated bonds are also more counter-cyclical. To the extent that those

aggregate factors underlying the risk premia on market debt also influence the cost of

external funds at the margin for banks, we should see interest rates increase more than

linearly (in the expected default loss) for lower-rated loans.

On the other hand, the premia on more risky loans may not be as cyclical as on

risky market debt if there is an implicit contract between banks and their borrowers under

which banks offer some degree of rate spread smoothing. In empirical analysis, we

account for the possibility of such implicit smoothing contracts by including lags of

maturity- and credit-risk-matched market spreads. Alternatively, some may interpret the

“stickiness” revealed by significant coefficients on the lagged market spreads as evidence

of credit rationing, in that bank loan spreads do not adjust as quickly because banks

restrict the type of borrowers who can obtain credit.20 One sign that may distinguish

between these two hypotheses is that rigidity due to rationing is possibly more

asymmetric relative to rigidity due to implicit spread smoothing. The intuition is that

banks are likely to shut out low-quality borrowers more swiftly when the aggregate

economy turns sour and default risk premia rise, and they are slower to extend credit to

lower quality borrowers when the overall economy improves.

Combining the comparative statics for the necessary loan rate , 1ˆ

i tZ + and the

maximal feasible loan rate , 1i tZ + , we see that parameter differences either across

19 Denote the denominator of expression (8) ( ) ( ) ( ), 1 , 1 , 1 , 1 , 1 , 1

ˆ ˆˆ ˆ ˆ1 1i t i t i t i t i t it it i tG h Z m a Zω ω ω+ + + + + + Λ ≡ − − + −

,

then ( ), 1 , 1 , 1ˆ ˆ 0i t it i t i tdZ da G ω+ + += − Λ < and ( ), 1 , 1 , 1

ˆ ˆ 0i t it i t i tdZ dm G ω+ + += Λ > . 20 See e.g. Berger and Udell (1992), although note that they regress spreads on Treasury yields instead of maturity- and credit-quality-matched market spreads.

17

borrowers or over time that push up the former also simultaneously push down the latter

(e.g., a higher m or a lower θ). The combined effect is to change the distance between

, 1ˆ

i tZ + and , 1i tZ + more than would be implied by the equilibrium condition for either rate

alone.

This result has the potential implication that a bigger percentage of small

borrowers may become credit constrained when the economy heads south. The intuition

is as follows: assume that large and small borrowers share the same distribution of θi’s

and ait’s, and the only difference between them is that small firms have higher mit’s.

Further assume that no firm was rationed during the good economic times. Then the

comparative statics derived above that , 1ˆ 0i t itdZ dm+ > while , 1 0i t itdZ dm+ < imply that

( ), 1 , 1ˆ 0i t i t itd Z Z dm+ +− < . In words, , 1

ˆJ tZ + for the marginal borrower J is closer to her

ceiling , 1J tZ + for small borrowers than for large ones. When a negative aggregate shock

hits the economy (i.e., Rt+1 falls), every , 1ˆ

i tZ + is raised even while the ceiling , 1i tZ + is

lowered. Given the marginal small borrower’s closer distance to her maximal feasible

loan rate, the same Rt+1 shock will push a bigger fraction of small borrowers beyond this

rate ceiling and shut them out of the bank loan market.

2.4 Empirical Specifications Implied by the Model

Following the model equation (3), the interest rate or spread regression can be

specified as follows:

, ,1 1( ) K N

ijt I I t t It I t j j k jt k n ijt n ijtk nd S D S D D X Zα β β β β γ λ ε

= == + + + + + + +∑ ∑ . (9)

The dependent variable dijt is either the yield or spread of loan i at bank j in

quarter t. The overall interest rate paid on a loan should arguably be the ultimate price

variable of interest, since it is the borrowing firm’s cost of capital (along with the shadow

rental price of its equity capital). Nevertheless, the spread of a loan rate over some base

rate, which is almost invariably tied to a market debt with minimal or no credit risk, is

often also analyzed for it is considered the “markup” paid by private sector borrowers.

18

SI in (9) denotes the loan size category dummies. Bank dummies Dj’s account for

bank fixed effects. A full set of time dummies (Dt, either yearly or quarterly) are also

included, to account for aggregate fluctuations not picked up by other control variables.

Our primary coefficients of interest are those on the interaction between loan size

dummies and time dummies, i.e., the βIt’s. These measure how the interest rates or

spreads on small loans relative to large ones vary from period to period. The null

hypothesis that the relative rates or spreads on small loans did not rise or fall significantly

during the Great Recession can be tested as follows:21

H0: mean of βIt = 0, t ∈[2008:Q1, 2009:Q4].22

We can also test if the average of βIt’s during this recession is significantly different from

its previous average. Alternatively, we can restrict βIt’s to be the same for all the periods

prior to the beginning of this recession, and allow it to jump to a different value since

then. The null then becomes that these two values for βIt are the same. We can also test if

the average βIt was significantly different from zero in the 2001 recession earlier in the

sample, and if the average βIt’s are the same for these two recessions.

As shown in the model, the loan interest rate or spread is influenced by a set of

bank- and loan-level characteristics, i.e., the vectors {Xjt}K×1 and {Zijt}N×1, respectively.

The primary purpose of bank-level controls is to account for unobserved time-varying

bank characteristics that influence µjt – a bank’s opportunity cost of funds inclusive of the

bank-specific markup. Some bank-level variables also help soak up cross-bank variations

in mit, which likely depends on a bank’s operating efficiency. Previous banking studies

suggest such relevant variables as bank size, liquidity ratio, capital adequacy, bank

profitability, quality of the loan portfolio, and a bank’s funding structure.

For instance, bank capital ratio can be regarded as a reduced-form measure of a

bank’s capital “shortfall,” to the extent that banks have similar target ratios for capital.23

21 One-sided tests can be used if we have reason to believe that the alternative hypothesis H1 should be that the relative rates or spreads on small loans rose or fell during this recession. 22 Given that the NBER dating committee has not yet announced the end date for this recession, we experiment with all the quarters between 2009:Q2 and 2009:Q4.

19

The bigger the shortfall, the higher the shadow cost of external financing, since banks

likely face frictions themselves in raising external funds. Another explanatory variable

aiming to capture time series variations in the opportunity cost of funds (µt in equation

(3)) is the interest rate or spread on market debt securities that most closely match the

repricing frequency as well as credit quality of a loan. As discussed above, if the lending

bank itself faced no additional frictions (due to information or agency problems), then

this repricing-frequency- and rating-matched market rate should be the exact cost of

funds for the loan; otherwise arbitrage opportunities would arise. On the other hand,

many banks raise funds via deposits exclusively, so their actual cost of debt financing

differs from the market rate relevant for private firms of comparable credit quality. To

capture such differences, we control for a bank’s funding sources, particularly the share

of deposits. Bank profitability can be a proxy for the bank’s operating efficiency, which

affects the monitoring cost.

The loan-level controls should include those loan attributes most relevant for

determining the interest rate. The model suggests the following variables: probability of

default or expected default loss, maturity and collateral status. The expected default loss

is rarely observable and thus approximated by discrete credit ratings. Since the repricing-

frequency- and credit-rating-matched market interest rate or spread is also included as a

control (as explained above), the loan maturity can be viewd as an extra control for

unobserved quality attributes of the loan. For instance, ceteris paribus, we may expect

loans of higher quality to have longer maturity.

As all previous studies have argued or demonstrated, elements of a loan’s terms

are jointly determined and so none can be considered exogenous and enter as explanatory

variables for the others in a structural manner. Also as will be discussed in greater detail

below, the internal credit rating of a loan is not strictly exogenous either. For our purpose,

the endogenous nature of the non-price loan terms as well as the credit rating is not a

concern in the usual sense because we do not attempt to interpret their coefficients as

structural. Instead, we include them as controls to account, as much as possible, for the

23 What should matter is presumably the deviation from a bank’s optimal target capital ratio. One can use procedures that explicitly estimate an individual bank’s target capital ratio, such as in Berger et al. (2008).

20

unobserved underlying true creditworthiness that influences the variation in interest rates

and spreads across loans. Imagine if these non-price terms were perfectly correlated with

credit quality differentials that are unobserved by the econometrician, then any significant

change in the coefficient on the loan size-category dummy during this recession would

not be contaminated by unobserved changes in the credit quality composition of the

borrower pool. Of course such “divine coincidence” is most unlikely. Any residual

changes in the composition of large vs. small borrowers’ quality during the recession will

load on the coefficient of the interaction term. This key issue will be discussed at length

in the empirical analysis in the next section.

III. Data and Empirical Analysis

4.1 Data Summary

The loan-level data used in this study are collected in the Federal Reserve’s

quarterly Survey of Terms of Business Lending (STBL). During the first full business

week of the middle month in each quarter, a sample of up to 348 domestically chartered

commercial banks and 50 U.S. branches and agencies of foreign banks are asked to report

terms of all the loans originated within that week. The survey overweights the largest

banks in that most of the top fifty banks are included and account for a bigger share in the

sample (in terms of both the number and dollar volume of loans) than their share in the

C&I loan portfolio of the banking industry as a whole.

For this study, we only use data reported by domestically chartered banks. The

primary reason is that the branches and agencies of foreign banks tend to originate C&I

loans in the largest size category while domestic banks originate mostly smaller loans.

The median size of C&I loans made by domestic banks is only near $45,000. In fact, on

average 90 percent of their loans have original principal less than one million dollars and

thus would be labeled small business loans. This makes domestic banks the suitable

sample given the focus of this study – to examine the dynamics of terms on small

business loans during the Great Recession.

The survey collects the following attributes of each loan contract: interest rate,

maturity, repricing frequency, intermal credit rating, whether it has prepayment penalty,

21

whether it is secured, and whether it is made under an existing commitment contract.24

Data of each bank’s internal credit rating of every loan are reported only since 1997.25

Two aspects of the rating data have especially important implications for our regression

specifications. First of all, the ratings are loan-specific and not fully exogenous in that

they are determined jointly with terms of the loan. The survey instructions state explicitly

that “definitions [of internal risk ratings] provided here take account of both the

characteristics of the borrower and the protections provided in the loan contract.”26 So

rating is particularly dependent on loan attributes such as whether it is secured, what is

the ratio between the value of collateral and loan principal, and loan covenants. For

instance, a borrower can improve the rating of her loan by putting up high-valued

collateral or accepting more restrictive covenants. In the model’s notation, this just means

that rating depends on not only borrowers’ type θi’s but also collateral ait and monitoring

cost mit. In contrast, individuals’ credit scores correspond to θi’s and are exogenous to

terms a consumer can receive on any incremental credit.

The second feature of these loan-level credit ratings is that they should, in theory,

be comparable across banks. The survey instructions describe in reasonable detail the

borrower credit conditions corresponding to each rating class. For instance, among other

criteria, Rating 1 (i.e., minimal risk) is to be assigned to a “customer who has been with

your institution for many years and has an excellent credit history.”27 Moreover, for loans

rated 1 and 2, the instructions specify the credit mapping to publicly rated corporate debt.

Ratings 1 and 2 are for customers with, respectively, AA and BBB or higher public debt

rating. Every respondent bank is instructed to enter the numerical designation that “most

closely matches the definition of the internal rating assigned to this loan,” but not the

institution’s own internal risk rating.

24 For documentation and more details, see data release E.2 at http://federalreserve.gov/releases/e2/. 25 See English and Nelson (1998) for a detailed account of the survey design for the rating data and a characterization of early vintages of the data. 26 In fact, loan terms and risk rating are in general jointly determined, according to our conversations with bank examiners and bankers. 27 The other criteria include that “The customer’s cash flow is steady and well in excess of required debt repayments plus other fixed charges… The customer has excellent access to alternative sources of finance at favorable terms… The collateral, if required, is cash or cash equivalent and is equal to or exceeds the value of the loan.”

22

Starting in 2003, the survey further distinguishes between formal commitments

and informal lines of credit. According to the instructions, a formal commitment is

defined as “a commitment for which a bank has charged a fee or other consideration or

otherwise has a legally binding commitment.” Otherwise, it is considered an informal line

of credit. Especially important for our purpose is that a formal commitment “is usually

evidenced by a binding contract, to lend a specified amount, frequently at a

predetermined spread over a specific base rate.”28 Furthermore, for each loan made under

a formal commitment, the banks since 2003:Q3 also report the date on which the

commitment contract itself was signed. Since the median and mean number of days

between the commitment and the drawdown were around 270 and 650 days in the

2003:Q3 survey, we have in the data commitments signed in 2001 and earlier.

For those commitment loans whose base rates are defined by the lending bank to

be a prime rate, a supplemental section asks the banks to record the exact prime rate used

on every day of the survey week. This prime rate can be either specific to the reporting

bank or as reported in the financial press.29 Figure 1a plots the distribution of the bank-

specific prime rates over time, along with the prime rate posted in the Federal Reserve’s

data release H.15, which has always been set at three percentage points above the Fed

funds target rate since 1994.30 This time series shows that the vast majority of loans are

priced off a common prime rate in every period, despite a fat right-tail – a few banks use

prime rates up to four plus percentage points above the modal prime rate.

The bank-level financial data are from the Consolidated Reports of Condition and

Income (generally referred to as the Call reports).31 These comprise balance-sheet and

income statements filed quarterly by all commercial banks operating in the U.S. to their

corresponding regulators.

28 For further details on distinctions between the two types of commitments, see the survey instructions, which can be downloaded from http://www.federalreserve.gov/reportforms/ReportDetail.cfm. 29 Such as the prime rate reported by the majority of the top 25 U.S. chartered banks and published in the Federal Reserve data release H.15, http://federalreserve.gov/releases/h15/. 30 Since the funds rate essentially hit the zero lower bound in December 2008, the prime rate has been held at 3.25% – three points above the upper bound of the zero to 25 basis points range for the funds rate. For the evolution of the relationship between this bank prime rate and the Fed funds rate, see Kobayashi (2009). 31 For the reporting forms and instructions, see http://www.ffiec.gov/ffiec_report_forms.htm. Data used in this study come exclusively from FFIEC 031 and 041.

23

4.2 Empirical Specifications for Regression Analysis

The specification (9) for the interest rate or spread regressions is recapped below:

, ,1 1( ) K N

ijt I I t t It I t j j k jt k n ijt n ijtk nd S D S D D X Zα β β β β γ λ ε

= == + + + + + + +∑ ∑ . (10)

The dependent variable dijt is either the yield or spread of loan i at bank j in

quarter t. In recent decades, a growing and now dominant share of bank loans are made

under outstanding contracts of commitments or lines of credit. For loans made under

informal lines, the yield is usually not pre-set but determined at the time of the drawdown

based on the spot market condition. In contrast, the interest rate on the funds drawn under

formal commitments is almost always specified as a base rate plus a fixed spread that was

chosen at the time when the commitment contract was negotiated. The base rate, on the

other hand, is left in most cases to vary with the spot market value of the interest rate to

which it is indexed, such as the prime rate or the LIBOR.

In light of the timing difference between loans under formal commitments and the

other loans (both new term loans and loans under informal lines), we analyze the yields

and spreads – pre-determined “markups” – on the former in separate regressions. The

time dimension in these regressions are indexed to the date when the formal commitment

was entered into, not when the loan was made. If every loan used the same base rate, then

loan yield and spread would be equivalent measures for the cross-section dispersion of

the cost of borrowing. However, as we will see, several different base rates are used in

practice, resulting in significantly different estimates in some specifications.

The size categories used for SI follows those in the Call reports, which classify all

C&I loans with original amounts of less than $1 million as a small business loan. These

loans are further divided into three size categories: I) below $100,000, II) between

$100,000 and $250,000, and III) between $250,000 and $1 million. There is the distinct

possibility that some small loans are in fact made to large firms, especially for loans

made under existing commitments since, with few exceptions, every drawdown is

recorded as a new origination. In addition, a bank participating in syndicated lending

deals only needs report the amount of its participation, not of the deal as a whole.

24

Nevertheless, there is no a priori reason to suspect that the discrepancy between loan size

and borrower size contains a cyclical component and thus biases our estimates.32

For our sample, one potentially more accurate way to classify the loans is to use

the size of the commitment. It seems reasonable to argue that, compared with the size of

individual drawdowns, the commitment size is better correlated with the firm size. In the

data, the correlation between loan size and the underlying commitment size is in fact

rather modest: mostly no more than 0.3. Following the convention, we apply the same

cutoffs to commitment size for classifying small business loans. Since individual

drawdowns under existing formal or informal commitments utilize on average about 15%

of the overall commitment balance, we also experiment with the following scaled-up

cutoffs for commitment sizes: I') below $500,000, II') between $500,000 and $1.25

million, and III') between $1.25 and $5 millions.33

The bank-level controls include the usual suspects: bank size, liquidity ratio,

capital adequacy, return on assets (ROA), quality of the loan portfolio, and the bank’s

funding structure. These help control for unobserved bank-specific variations in the cost

of funds over time. Bank capital ratio here serves as a proxy for the shadow cost of

equity. In addition to the more standard measure of the ratio of tier-one regulatory capital

over risk-weighted assets, we also experiment with the ratio of tangible common equity

over total risk-weighted assets, which has been found to better reflect the true capital

adequacy of banks during this financial crisis.34 Table 1 details the repricing-frequency

and credit-rating-matched market reference interest rate or spread for loans in each rating

class; these serve as controls for aggregate variations in the opportunity cost of funds

over time. In addition, to capture the deviation of a bank’s cost of debt financing from the

market reference, we include a bank’s funding composition, which is defined as the share

of deposits in total liabilities.

32 Moreover, according to an informal survey conducted recently by Federal Reserve Board staff, most of the banks whose C&I portfolios are concentrated in small loans are in fact engaged primarily in lending to small businesses. 33 There is anecdotal evidence that a non-trivial fraction of small business loans are above $1 million. See e.g., http://dpc.senate.gov/pdf/wh/treasury_smallbus_recession.pdf. 34 See e.g. Duffie (2009).

25

Portfolio quality is measured as the share of non-performing loans either within

the C&I portfolio or the entire loan portfolio. The former may be correlated with

unobserved quality differentials (within a rating class) in C&I portfolios across banks,

while the latter may contain additional signal related to the unobserved capital pressure

on the bank.

Given that the dependent variable should have no time trend in steady state, we

use a normalized measure of bank size – the share in total assets of all domestically

chartered banks in a given quarter. Alternatively, dummy variables for bank size

categories are used. Liquidity is defined as the ratio of cash and market securities to total

assets. Alternatively, it can be measured as the share of deposits in transaction accounts.

According to the literature on banks as providers of liquidity insurance (see e.g. Kashyap

Rajan and Stein 2002 and Gatev and Strahan 200?), banks with a high percentage of

transaction deposits have comparative advantage in liquidity insurance and thus may

offer either lower spreads on average or better spread smoothing over the business cycle.

As a measure of bank profitability, ROA serves as a proxy for the bank’s operating

efficiency, which affects the monitoring cost.

Among the loan-level controls, the credit ratings enter as dummy variables, i.e.,

there are five binary dummies corresponding to the five rating classes, respectively. This

measure allows different ratings to have flexible influence on the loan interest rate or

spread. Another binary variable identifies if a loan is secured (equal to one if the loan is

secured and zero otherwise). Unfortunately there is no information on the collateral value

relative to the loan principal. Since over 30% of the loans have no stated maturity, we

introduce a missing-maturity dummy that equals one for such loans to avoid losing them

and set their maturities to be the longest.35 We also include a dummy variable identifying

floating- vs. fixed-rate loans (equal to one if the loan rate is floating and zero otherwise);

over 90% of the loans in the sample are floating-rate. In pooled regressions that include

all types of loans, a commitment status dummy is added (equal to one if the loan is made

under an existing commitment or line of credit and zero otherwise).

35 According to the survey instructions, “many drawdowns priced off of the prime rate have no stated maturty...” So the missing maturity issue is more relevant for regressions with prime-based loans only.

26

We also experiment with lags of the matched market interest rate or spread, to

account for the possibility that banks may have implicit agreements with their customers

to smooth interest rates over time. Alternatively, some (e.g., Berger and Udell, 1992)

have interpreted such “stickiness” in bank loan interest rates as evidence of credit

rationing. This is likely less a concern for our analysis, where we are able to control for

the credit rating of each loan.

4.3 Results of Loan Interest Rates and Spreads Regressions

We first examine how interest rates on small business loans vary over relative to

rates on large business loans, especially how the relative rates behaved during this

recession. To better approximate the behavior of loan terms for the population of all

domestic banks, we scale up the survey sample using bank-specific scaling factors

calculated by the Federal Reserve Board staff.36 The sample for most regressions starts in

1997:Q2, because the rating data are only available since then. The latest quarter in the

data set is 2010:Q1. There are initially over one million loan-observation for this sample

period, and slightly over 950 thousands remain after we drop those observations with

missing values for any of the variables used in the regressions. (The number of

observations entering each specific regression will be reported separately, along with the

coefficient estimates.) In all the regressions, standard errors are clustered by bank.

The bank-level controls are based on the financial data from one quarter prior to

the survey quarter. The sample is adjusted for bank mergers and acquisitions as follows:

the target and acquirer for each deal are treated as separate entities till the quarter prior to

the effective date of the merger, then the merged bank is treated as yet another distinct

entity. Table A.1 in the appendix details the definition of the variables used to construct

these bank-specific controls. It also defines the loan-specific reference market spread,

based on the market security whose maturity is closest to the loan’s next repricing date

and whose rating best matches the comparable market securities if specified in the survey

36 These factors take into account the discrepancy between the share of C&I loans accounted for by banks in a particular size stratum in the sample vs. in the population of banks according to the Call reports. For large banks that report only the originations on some but not all business days in the survey week, the scaling factors also adjust for the partial reporting.

27

instructions. So, for loans rated 1, the reference securities are AA-rated market bonds or

A1/P1 commercial paper if the maturity is less than a year. For loans rated 2, the

reference is A- and BBB-rated market bonds or A2/P2 commercial paper. Since the

comparable market rating classes are not specified for loans rated 3 through 5, we choose

BB, B and CCC bonds as the respective market reference.

As shown in Table 1, which reports the summary statistics for the variables that

enter the regression analysis, slightly over 90 percent of the loans have initial principal

amount less than the $1 million cutoff and thus would be classified as small business

loans. Among these, over 60 percent have balance less than $100,000 – in fact the median

loan size is only $45,000 – and the rest about evenly divided between the remaining two

size categories.

Nearly 90 percent of the loans have floating rates, and around 80 percent are

secured. Nearly 30 percent of the loans have no stated maturity, which are most likely

drawdowns priced off of the prime rate, judging by the survey instructions. Among the

rest, the median and mean maturity is around 270 days and 470 days, respectively. This

indicates that the majority of bank loans have maturity less than one year.

In terms of the distribution of individual loan credit ratings, the bulk are rated 3

(i.e., Moderate risk) or 4 (i.e., Acceptable risk): about 45% rated 3 and 36% rated 4. A

tiny fraction (2%) are in rating class 1 (i.e., Minimal risk), and about equal percentage

(8%) in rating classes 2 and 5. This suggests that few bank customers satisfy the high

standards laid out in the instructions for rating 1 borrowers. Rating 5 should be rare too,

especially among new loans, since it applies to loans that must immediately incur capital

charges. Data confirm that rating 5 is indeed minimal among new loans – by and large

less than one percentage in every period and, not surprisingly, hardly variable over time.

By comparison, the somewhat higher share of commitment loans rated 5 shows clearer

comovement with the business cycle – rising during both recessions in the sample period.

It in fact rose more around 2001 than during this Great Recession. Given the low share of

rating-5 new loans, we omit them as a robustness check, and this has virtually no effect

on the parameter estimates.

28

4.3.1 Baseline Regressions: All Loans

First, we report the results of a baseline regression of loan yields that includes all

loans – new term loans as well as loans made under commitments or lines of credit.

Loans with original balance greater than $1 million are the omitted group, and 1998:Q1 is

the omitted quarter. Figure 2a plots the coefficients on the interaction terms between

quarter dummies and loan size category dummies (along with the one-standard-deviation

band). Table 2 presents coefficient estimates on the rest of the explanatory variables.

The positive and significant coefficients on the three small-loan size dummies is

consistent with the prior suggested by the model – small loans on average carry a higher

rate. Note, however, that the relationship is not monotonic – the relative rate bottoms for

loans in the $100,000-to-$250,000 size bin. This is because, with a full set of interaction

terms between loan size dummies and quarter dummies, these coefficients do not measure

the relative rates on average but only for the base period (i.e., 1998:Q1). In general, the

relative rates are monotonic on average but not necessarily so in any given quarter, as can

be seen from the relationship among the coefficients on the time-interaction dummies for

the three small-loan size bins respectively.37

None of the bank-level controls are significant, except for the capital ratio. The

significant positive coefficient may be due to the fact that small banks tend to charge

higher than average interest rates – the coefficient on normalized bank size is negative

albeit insignificant – and hold more capital. The repricing-frequency- and credit-quality-

matched market yield does enter positive and significant. However, the magnitude is

small – for a one-percent-point increase in the market yields, bank loan yields only rise

4.5 basis points on average. This could be because banks adjust loan rates with

substantial lags, or banks alter the composition of their borrower pools so that there is

time-varying credit rationing.

Among the loan-level controls, credit ratings have the intuitive effect on yields –

the higher the rating, the lower the yield. Relative to loans rated 1, which is the omitted

37 The monotonic increase in the relative rate of small loans is easily confirmed in a regression without interaction between loan size and time dummies. Relative to the above-million-dollar loans, yields are higher by 0.64, 0.89 and 1.30 percentage points, respectively, for small loans in decreasing size groups .

29

class, yields rise an almost uniform 50 basis points for every notch of increase in the

rating number (i.e., lower credit quality), except for from rating 3 to 4, which brings only

an uptick of 30 basis points in yields. Fixed-rate loans carry marginally higher yields than

floating-rate ones: only 8 basis points. By comparison, yields on secured loans are higher

by 14 basis points. As discussed in the model section, a positive correlation between

secured status and yield can arise loans of greater unobserved risk are more likely to be

required collateral. Maturity has marginal impact on yields – an additional year in

maturity would raise the yield by less than a basis point.

Now we turn to time series variations in yields on loans of different sizes. The top

left panel of Figure 2a indicates that there has been a downward trend in the average yield

charged on the smallest C&I loans (i.e., less than $100,000), which was interrupted by the

2001 recession and then petered out since 2006. Their spreads were on average higher

until 2004 and lower since then, with a cumulative decline of about 80 basis points.

During the financial crisis and the ensuing recession, yields on the smallest loans did not

rise more than on loans larger than $1 million (i.e., the omitted size category). However,

if we took the downward trend prior to the onset of the crisis to be the baseline, we would

conclude that the relative yield on these loans had in fact increased during this crisis and

recession.

Similarly, the relative spreads on the other two categories of small loans have

trended down as well (as shown in the top right and bottom left panels), albeit more

modestly. Unlike the smallest loans, the downward trend in relative yields for these two

small loan categories was essentially uninterrupted by either of the recessions in the

sample. By comparison, the bottom right panel shows that the average yield on loans

larger than $1 million (i.e., coefficients on the time dummies) exhibits little trend and its

variations over time are dominated by two persistent humps, one around the 2001

recession while the other around this recession.

We conduct Wald tests of the null hypothesis that the relative yields on small

loans did not change significantly during this recession, i.e.,

H0: mean of βIt = 0, t ∈[2008:Q1, 2009:Q4], I = 1, 2, 3.

30

As can be inferred from the plots in Figure 2a, the tests indicate that yields on the below-

$100,000 loans rose less in this recession relative to yields on the above-$1-million

loans.38 By comparison, the relative change in yields on the other two categories of small

loans were indistinguishable from zero. Since the bulk of loans belong to the smallest size

category, the behavior of their relative yields dominates the unweighted result for all

small loans. Therefore, for small loans as a whole, their yields on average rose less than

large loans’ during this crisis-recession.

Given the above findings of the relative change in yields between large and small

loans, it is no surprise that qualitatively the same result emerges when we run the same

regression for the yield spread over a common base rate (Fed funds rate) on the left hand

side. Yet again, we obtain the result that the spreads on small loans on average rose less

than those on large ones during this downturn.

These pooled regressions, however, suffer from important mis-specifications

because they ignore two special institutional features of loans made under commitments.

First of all, the information content of yield differs qualitatively between new term loans,

drawdowns under an informal line of credit and most drawdowns under a formal

commitment. As discussed above, the entire yield on a new loan or loans under an

informal line is determined according to the spot market condition when the loan is made,

whereas the spread on loans under a formal commitment is typically fixed at the level

pre-set at the time of the commitment. This means the spread part of the yield on formal

commitment loans is “stale” in that it was chosen according to conditions of the borrower

as well as the aggregate economy at the time when the commitment was extended, not

when the drawdown was granted. So it is incorrect to regress either such a spread or the

corresponding yield on variables indexed to the later time of the drawdown.

Another typical feature of formal commitment contracts is that they specify which

type of base rate, such as a prime rate or the LIBOR, will be used in calculating the yield

on drawdowns. The fact that the pooled regressions ignore this contractual feature turns

out to significantly alter the conclusion regarding the relative change in yields and

spreads between large and small loans. As we will show below, small loans are largely

38 This test result is essentially the same as that in Kwan (2010).

31

indexed to a prime rate, whereas large loans are more often indexed to the LIBOR.

During the crisis and recession period, the LIBOR rose to unprecedented heights and

persisted at those levels for months. So we suspect that the bigger increase in yields on

large loans is mostly attributed to the extraordinarily high yields on drawdowns under

formal commitment indexed to LIBOR, as will be suggested by further analysis below.

4.3.2 Regressions of New Loans vs. Loans under Commitments

First we address how the pre-determined nature of spreads on loans under formal

commitments influence the estimate of the relative change in yields and spreads between

large and small loans. Our solution is to run separate yield and spread regressions for new

vs. commitment loans. Since, like new loans, loans under informal lines of credit mostly

have terms set ex post at the time of the drawdown, we would ideally group new and

informal-line loans together. Unfortunately, the survey only started distinguishing

between informal lines and formal commitments in 2003. On the other hand, only about 4

percent of the loans are under informal commitments. So for the sample from 1997 to the

present, we regress spreads on new loans by themselves. For the subsample from 2003,

we consider two regressions: one for new and informal-line loans together, and the other

for formal-commitment loans.

The second column of Table 2 reports the new-loans-only regression since 1997,

and Figure 2b plots the coefficients on time and time-small-loan-interaction dummies.

One clear message is that the relative increase in rates on the smallest loans during this

recession is now insignificantly different from zero, just as the relative rates on the other

two sets of small loans. Meanwhile, the coefficients on the other explanatory variables

remain qualitative the same. This suggests that for term loans originated “on the spot,”

whose rates should be determined mostly by market and borrower conditions at the time

of the origination, there was no significant change in the relative yield between large and

small loans.

This pattern remains essentially unchanged for the post-2003 subsample that

includes new and informal commitment loans, which are presented in the third column of

Table 2 along with Figure 2b. This is perhaps not surprising given the small fraction of

32

informal commitment loans, although it also indicates that the estimates for new loans are

reasonably stable over time. Together, these two sets of results indicate when loan rates

are determined at the time of origination, no significant change in the relative relationship

between large and small loans can be detected for quarters during the Great Recession.

Spread and Base Rate – The Financial Crisis and LIBOR

We next consider the second consequential aspect of typical contracts of formal

commitment to lend: the type of base rate used to calculate the yield is set in the

commitment contract and generally remain unchanged. A variety of rates are used in this

capacity, although all share one common trait – considered credit-risk-free or virtually so

under nearly all circumstances. According to the data on the specific type of base rate

used on each loan, which are only available between 1986:Q1 and 2003:Q2, the most

popular base rate is a prime rate, while the LIBOR typically ranks the second. In addition,

the Fed funds rate, other domestic money market rates, and other unspecified rates are

used. The historgram of different types of base rates in Figure 1b reveals a clear pattern:

prime rates are used noticeably more often on loans smaller than one million dollars,

while the LIBOR rate is used more often on larger loans.39 And the share accounted for

by either LIBOR-based or prime-based loans is stable within large and small loan size

categories over that sample period. By comparison, the incidence of these two base rates

does not differ nearly as much across banks of different sizes.

So one reason that interest rates rose more on large loans than on small ones

during this crisis-downturn could simply be mechanical. The LIBOR spiked to

extraordinary height during the peak of the crisis and persisted at those elevated levels for

months. It resulted in much higher yields on large loans made under existing formal

commitments that had set the LIBOR as the base rate. Since a noticeably higher fraction

of large loans use LIBOR as the base rate, while small loans are more likely to use the

prime rate or CD rates, shocks to the LIBOR showed manifested as bigger increases in

yields on large loans.

39 This is consistent with the pattern for loans to large corporations reported in the DealScan database, where LIBOR is the most commonly used base rate. See e.g. Ivashina and Scharfstein (2008).

33

The finding above of insignificant relative rate changes during this recession

between small and large new loans is consistent with this conjecture. For a new

origination, the bank and the borrower can negotiate about the entire yield without regard

to any prior contractual constraints as in the case of loans under formal commitments.

Specifically, for commitment loans, large ones on average would be more subject to the

adverse impact of abnormal behavior of LIBOR than small ones, whereas for new loans,

this would not be the case. If this interpretation is correct, then the yields on large

drawdowns under formal commitments should exhibit the steepest relative increase

during the months when the LIBOR was elevated. When the same yield regression is run

on commitment loans only, the quarterly pattern of coefficients on the time-size-dummy

interaction terms is mildly consistent with this hypothesis.

Under the hypothesis that the crisis-induced shock to LIBOR base rate was

mostly, if not solely, responsible for the steeper increase in yields on large loans, we

should also expect spreads – i.e., yields net of base rates – to show no significant relative

change between small and large loans during the crisis. This test, however, can only be

conducted on loans priced off of prime rates, since only for such loans are data on base

rates available consistently from 1997:Q2 onward. Fortunately, throughout the sample

years, a fairly steady majority – around 80% – of the loans are priced off of prime rates.

On the other hand, an additional drawback is that the share of large loans is even smaller

in this subsample, down from 8% to 4%.

Given the timing of the spread decision for formal commitments as discussed

above, we also regress their spreads separately from spreads on new loans (together with

informal commitment loans or without).40 Column (1) in Table 3 reports the coefficient

estimates from the regression of spreads on all prime-based loans, with all explanatory

variables dated by the time of the loan (i.e., not the time of the commitment even for

commitment loans). Unlike in the yield regression, the coefficients on time-size-dummy

interaction terms no longer average to significantly negative, as can be seen in Figure 3a.

40 Compared to commitment loans, it is less clear to the borrower what exactly is the meaning of spread on a new loan, since what she should care about is the cost of capital, which corresponds to the yield. The spread on a new loan can be meaningful for the lender, to the extent her cost of funds covaries closely with the base rate. In the STBL data, 40% of new loans report a prime rate being the base rate.

34

This result is consistent with our conjecture about the role of LIBOR in boosting yields

on more of large loans. By comparison, no significant difference is found for either rate

or spread changes between large and small new loans (with the latter reported in column

(2) in Table 3).

For spread regressions to be consistently specified for loans made under formal

commitments given the timing convention of such contracts, all the bank-level controls

should be matched to the date when the commitment was signed, i.e., based on financial

data from the prior quarter-end. Likewise, the maturity- and rating-matched market

reference spread on the right hand side should be from the week prior to the signing of

the commitment, instead of the date of the drawdown. For the same reason, loan-specific

terms that are assessed at the time of the drawdown and after the commitment terms

should not enter the spread regression. In our data, these include loan-specific rating and

possibly maturity as well. Instead, we invert the regression and use the following two-

stage procedure to gauge the predicative power of spreads for credit rating, as well as the

impact of recession on credit rating, which may differ across loan size categories.

It is natural to ask if the use of either a prime or the LIBOR rate indicates certain

sample selection that can bias the regression results. We are unaware of any systematic

principals governing the base rate choice for a loan with a specific set of characteristics.

From informal conversations with former loan officers, we learned of one explanation for

some large borrowers’ preference for the LIBOR as base rate. They favor the LIBOR

because the market for LIBOR-based interest rate swaps is considerably deeper than that

for prime-based swaps. Such borrowers can thus achieve the objective of borrowing at a

fixed rate over an extended period more cheaply by obtaining a floating-rate loan from a

bank while simultaneously entering into a swap agreement with a third party. We can

think of no obvious reason why this rationale for choosing the LIBOR as the base rate

should bias our finding.

By comparison, the choice of the prime rate has more a potential of being

correlated with unobserved compositional changes in the quality of the borrower pool.

The prime rate used to be reserved for each bank’s largest and most creditworthy

borrowers (see e.g. Lang and Nakamura, 1985), but its elite status has gradually

35

dissipated since the mid 1980s as a growing fraction of those privileged bank borrowers

migrated toward the capital market. Nevertheless, certain residual prestige in the use of a

prime rate remains relevant nowadays for lending to small firms. This could help explain

why, among loans priced off a prime rate, there is no significant change in the spread

paid on small loans relative to large ones during both recessions in the sample period.

One last caveat of the STBL data is that there is no information on any of the fees.

Strictly speaking, a borrower’s cost of capital equals the all-in cost of each loan contract,

which includes various fees (such as the origination fee paid upfront) in addition to the

interest rate. So the absence of fee data in the STBL can be especially problematic for

loan commitments and lines of credit, since the overall cost of either type of contract

typically comprises a bigger share of fees, routinely a fee on the unused portion and

sometimes also an annual fee on the entire line.

To the extent the heterogeneity in these unobserved fees is largely across banks

and reasonably stable over time, the bank fixed effects should take care much of it. But if

the fees vary more across loans within a bank than across banks, then the inability to

control for fees associated with each loan can bias our results and even reverse them. For

instance, it is possible that even though small loans on average saw no bigger increase in

their loan interest rates than the large loans during this recession, the all-in cost of

funding in fact rose more for small borrowers if they had to pay higher fees. Nonetheless,

there is no a priori reason to expect the fee portion of borrowing to rise more for small

borrowers than for large ones during bad times. Nor are we aware of anecdotal evidence

to such effect. In fact, for loans made under existing commitments, which constitute the

bulk of our data, the marginal cost of funds equals the interest rate net of the fee on the

unused commitment. So if small borrowers faced higher fees, their marginal cost of funds

would actually be lower.

4.4 Maturity and Collateral Status

To examine if, compared with large loans, small business loans have seen a more

pronounced shortening of maturities, we regress a loan’s maturity (measured in days) on

36

a similar set of explanatory variables as in equation (10):41

, ,1 1( ) K N

ijt I I t t It I t j j k jt k n ijt n ijtk nm S D S D D X Zα β β β β γ λ ε

= == + + + + + + +∑ ∑ . (11)

mijt is the maturity of loan i at bank j in quarter t, measured in days. The right

hand side variables are defined the same as in (10), except that loan-level controls {Zijt,n}

no longer include maturity.

Table 4 displays the maturity regression results, with the three columns

corresponding to the three cuts of the sample as for the yield and spread regressions

above. First, with all loans, coefficients on the loan size dummies along with those on the

interaction terms imply that small C&I loans tend to have shorter maturities. This is

especially so for the smallest loans, although the difference in maturity across size groups

is often insignificant. Furthermore, there is little variation in maturity during either of the

two recessions in the sample period, except perhaps in 2008Q4, when maturity on

average increased. Nor is there much relative change in maturity across different loan

size categories. The Wald tests by and large cannot reject the hypotheses that coefficients

on the interaction terms are jointly significant during the recession periods, or that their

cumulative values are no different from zero.

All the bank controls are again insignificant. Among the loan controls, lower

rating class generally shortens maturity. This effect is similar for loans rated 3 and 4, the

two rating classes accounting for the bulk of loans. Maturity is, perhaps not surprisingly,

shortened significantly for rating 5. Secured loans, on the other hand, tend to have longer

maturity. This suggests that borrowers put up collateral not only to obtain more favorable

interest rates but likely also longer maturity.

When we restrict the sample to include only new loans, the coefficient estimates

are qualitatively similar. The one major difference is that in the new-loan sub-sample, the

negative impact of capital ratio becomes significant. In general, a negative relationship

41 Obviously, only those observations with non-missing values for maturity can enter these regressions. Even though maturity can only take on non-negative values, the OLS regression here seems a reasonable approximation – only a small fraction of fitted values are negative. Potentially more problematic is the interpretation of observations with stated maturity equal to zero. These loans have indefinite maturity, which can be either rather short or rather long. In addition, those observations with missing maturity data are more prevalent in prime-based loans and thus may skew the quality composition of the observed loan pools. We will continue to explore these issues.

37

between maturity and bank capital emerges from all three regressions. This may indicate

that longer loans are perceived as riskier and banks tend to hold more capital in response.

So, these regressions suggest that banks tend not to adjust the maturity dimension

of C&I loans, including the small loans. This is in contrast to the dramatic shortening of

maturity in the commercial paper market during the peak of the financial crisis following

Lehman Brother’s bankruptcy. There is certainly no evidence that banks have shortened

the maturity more on small C&I loans during this recession.

We next consider the question if banks have tightened the collateral requirement

more on small C&I loans in this downturn. The STBL data only records whether a loan is

secured or not; there is no information on the collateral value, nor the loan-to-value ratio.

We thus run a probit regression of the binary dummy of a loan’s secured status, which

equals one if a loan is secured, on the same set of explanatory variables as in (11):

, ,1 1P( 1) ( ( ) )K N

ijt I I t t It I t j j k jt k n ijt n ijtk nCollateral S D S D D X Zα β β β β γ λ ε

= == = Φ + + + + + + +∑ ∑ . (12)

Table 5 reports the raw coefficient on each explanatory variable from (12), while

Tables 5a and 5b report the marginal effect of the interaction between quarter and small-

loan size category dummies during the recession quarters. The three columns in Table 5

again correspond to the three cuts of the sample as for the previous regressions. First, for

all loans, the significantly positive coefficients on the three small C&I loan size dummies

indicate that small loans are more likely to be required to pledge collateral, especially

those in the smallest size group. This is consistent with the idea that smaller businesses

are more informationally opaque and therefore banks require more guarantees to extend

credit. By comparison, this monotonic (inverse) relationship between loan size category

and the probability of posting collateral disappears for new term loans as well as loans

under informal lines of credit, as indicated by the coefficients on the interaction terms in

the other two columns. One possible explanation is that banks use collateral to mitigate

expected loss on loans made under terms pre-set at the time when commitment contracts

were signed, but set terms on new loans jointly at the moment when the lending decision

is made and so can choose to grant credit only to those small borrowers whose credit

quality is above a certain threshold even absent collateral.

38

Among the loan-level controls, it is interesting to note that lower credit rating

grades are associated with lower likelihood of having pledged collateral. This seems

counter-intuitive at first glance, but it can be an outcome of the joint determination of

collateral and rating. Specifically, borrowers who consistently put up collateral are

awarded with the two best rating class – 1 and 2.

In recession periods, the probability of collateral being required tends to increase,

as is evidenced by the positive coefficients on the recession year dummies. However, as

shown in Table 5a, marginal effects of the interaction between small loan and recession

quarter dummies for all loans imply that the smallest business loans in fact became less

likely to pledge collateral than the larger loans. Specifically, the biggest negative

coefficients for the smaller loans are reached in 2008Q3 and 2009Q1, around the quarter

of the most critical episode of the crises. That is, likelihood of collateral requirements for

loans smaller than $100,000 dropped by 12 and 13 percentage points compared to loans

bigger than $1 million in the first week of August 2008 and February 2009, respectively.

In contrast, the probability of collateral requirements changed by essentially the same

magnitude for loans of all sizes in the 2001 recession.

In contrast, among new loans only, the probability of pledging collateral rose

somewhat more for small loans, especially those between $100,000 and $250,000, as

indicated by the coefficients on the interaction terms in Table 5b. However, for small

loans in all three size sub-groups, the relative increase in the probability of posting

collateral during this recession is on average hardly more than the increase seen during

the 2001 recession.

Taken together, the above findings suggest that small businesses have by and

large experienced hardly more tightening in either the price or the non-price terms of

their bank loans than large businesses since the onset of this recession. This poses

challenges to the popular policy initiatives aimed at making credit more cheaply and

readily available to small businesses. If the contraction of small business loan volume is

mostly attributable to diminished borrowing need to finance working capital, inventories

and the like because small firms saw decreased demand for their products during the

downturn, then policy initiatives designed to encourage lending to small firms per se by

39

offering government assistance may not be as effective as hoped by some. Nevertheless,

even absent credit supply constraints, these measures can still stimulate final demand

because they lower the cost of capital for small businesses, which will therefore be

willing to invest more, all else equal (e.g., the same expectations of sales).42 In addition,

there may be a decent multiplier on the first round of investment expenditures. However,

given the survey evidence that the majority of small businesses cite weak sales as their

foremost worry, it is hard to imagine that these fiscal subsidies will be able to reduce the

cost of capital for small firms by such a magnitude that they sufficiently offset the drag

from the slump in sales. This in turn implies that there will remain much heavy lifting for

monetary policy, whose efforts should continue to focus on stimulating aggregate

demand in general.

IV. Conclusion

A public policy issue that has gained prominence in recent quarters is whether

credit constraint has been largely responsible for the unusually severe net job losses

suffered by small businesses relative to large firms since the onset of the Great Recession.

The answer to this question can have important implications for the kind of policy

solutions that will likely be most effective in stimulating recovery and growth of small

businesses, which many believe are crucial for the much needed job creations. This study

develops a model of the pricing of bank loans, and applies it to analyze the dynamics of

price and non-price terms on small business loans relative to large loans over the past

decade or so. It then compares the relative terms on small business loans before and

during this recession, to help assess if small business loans have experienced greater

tightening of both price and non-price terms during the Great Recession.

Overall, we find that it is important to account for the special institutional features

of bank loans that are drawdowns under existing formal commitments to lend. Once we

42 In theory, lower cost of capital should encourage investment, ceteris paribus. However, research has generally found that the user cost of capital, if measured based on some type of risk-free rate, is insignificant in investment equations. On the other hand, a few more recent studies, such as Philippon (2009) and Gilchrist, Yankov and Zakrajsek (2009) find that firm-specific cost of capital that takes into account the risk premium on corporate debt has significant explanatory power for real investment. So to the extent that these subsidies lower the all-in cost of funds considerably for the borrowers, they should stimulate investment by small firms.

40

take in account that interest rates on most of these loans equal a pre-chosen floating base

rate plus an also pre-set but fixed spread, there is little evidence that the small business

loans experienced any greater tightening in either the yield, spread or the non-price terms

than large business loans during this so-called Great Recession.

Furthermore, our preliminary analysis to detect signs of credit rationing has also

turned up negative. We find that, contrary to the usual intuition for rationing, the share of

new term loans relative to loans made under commitment in fact rose during this

recession. This can be the perverse effect of a deep and protracted recession, during

which banks became more stringent in granting new commitments than in originating

new term loans. If this was a relevant factor, then we should expect to observe a longer

average time elapsed between the date of the commitment and the date of the drawdown

rose during this recession. Our examination shows that this average has indeed risen since

the onset of the recession, but not significantly so.

In summary, our findings suggest that credit availability is probably not the chief

hindrance to the recovery of small businesses. This implies that policy measures that

narrowly aim to subsidize credit supply to small businesses may not be that effective in

encouraging the expansion of existing small firms or the creation of new ones. They will

in turn disappoint in their efficacy to stimulate job growth. Instead, policy efforts should

continue to concentrate on stimulating aggregate demand.

41

References

Berger, Allen N. and Gregory F. Udell (1992). “Some Evidence on the Empirical Significance of Credit Rationing,” Journal of Political Economy, 100(5), p. 1047-1077.

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Bernanke, Ben S., Mark Gertler, and Simon Gilchrist (1999). “The Financial Accelerator in a Quantitative Business Cycle Framework,” in Bernanke, Ben S., Gertler, Mark, and Gilchrist, Simon (eds.), Handbook of macroeconomics. Volume 15(1C), 1999, p. 1341-93. Amsterdam; New York and Oxford: Elsevier Science, North-Holland.

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43

Table 1. Summary statistics of regression variables Variable Description Obs Mean Std. Min MaxspreadY Spread of effective interest rate to prime rate 1568309 0.5449 1.26419 -9 13.76primeb Dummy variable for prime-based loans 1568309 0.421 0.49371 0 1primerate Prime rate listed by lending institution 1568309 6.3711 1.99411 2.23 13.4qtbl6138_1 Prime based pricing rate 673726 0.7694 0.42123 0 1qtbl6138_2 Fed Funds based pricing rate 673726 0.0104 0.10164 0 1qtbl6138_3 Other Domestic Money Mkt based pricing rate 673726 0.018 0.13293 0 1qtbl6138_4 Foreign Money Mkt based pricing rate 673726 0.0736 0.2612 0 1qtbl6138_5 Other based pricing rate 673726 0.1285 0.33469 0 1fedfunds Federal Funds Rate 1568309 3.328 2.01541 0.11 6.51cpaa AA Commercial Paper rate 1568309 3.3835 1.98426 0.13 6.52us0003m 3 month Treasury bill yield at constant maturity 1568309 3.0672 1.88894 0.056 6.19amount Loan Amount 1568309 399.09 3219.45 5.286 790454.3smb Dummy variable for loans less than $1,000,000 1568309 0.9456 0.2269 0 1smb_1 Dummy variable for loans less than $100,000 1568309 0.6874 0.46356 0 1smb_2 Dummy variable for loans $100,000 - $250,000 1568309 0.1494 0.35652 0 1smb_3 Dummy variable for loans $250,000 - $1,000,000 1568309 0.1087 0.31128 0 1informal_com Dummy=1 if loan w as made under an informal commitment 1568309 0.4018 0.49027 0 1new loan1 Dummy=1 if loan is a new loan made under no commitment 1568200 0.1237 0.32924 0 1comloan1 Dummy=1 if loan is made under existing commitment 1568200 0.8763 0.32924 0 1rating_1 Dummy for loans rated 1 1199003 0.0199 0.13983 0 1rating_2 Dummy for loans rated 2 1199003 0.0899 0.28604 0 1rating_3 Dummy for loans rated 3 1199003 0.4483 0.49732 0 1rating_4 Dummy for loans rated 4 1199003 0.3575 0.47927 0 1rating_5 Dummy for loans rated 5 1199003 0.0843 0.27786 0 1floating Dummy=1 if loan has a f loating rate 1568309 0.8975 0.30336 0 1secur Dummy=1 if loan is collateralized 1568309 0.8207 0.38357 0 1maturity Days until maturity 1203641 466.42 693.87 0 26449xYield Market Debt security yields (time to re-pricing)* 1199003 7.0744 0.86325 5.05 8.88xspread Market Debt Security Spreads (time to re-pricing)* 1166044 1.8753 0.79992 0.45 4.68Liquid Ratio (cash+securities+trading assets)/assets 1568309 0.2246 0.08971 0.017 0.935264ROA quarterly income/assets 1568309 0.0026 0.00394 -0.19 0.23972Capital Ratio capital/assets 1568309 0.0941 0.0225 6E-04 0.561965Bank Size assets/aggregate banking sector assets 1568309 0.0147 0.0187 8E-07 0.138793NPL Ratio non-performing loans/assets 1568309 0.0088 0.0085 0 0.327136y_1998 Dummy for loans made in 1998 1568309 0.0868 0.28151 0 1y_1999 Dummy for loans made in 1999 1568309 0.0899 0.28606 0 1y_2000 Dummy for loans made in 2000 1568309 0.0791 0.26996 0 1y_2001 Dummy for Loans made in 2001 1568309 0.0792 0.27002 0 1y_2002 Dummy for loans made in 2002 1568309 0.0741 0.26195 0 1y_2003 Dummy for loans made in 2003 1568309 0.0726 0.25944 0 1y_2004 Dummy for loans made in 2004 1568309 0.0827 0.27543 0 1y_2005 Dummy for loans made in 2005 1568309 0.0744 0.26244 0 1y_2006 Dummy for loans made in 2006 1568309 0.0905 0.28687 0 1y_2007 Dummy for loans made in 2007 1568309 0.084 0.27735 0 1y_2008 Dummy for loans made in 2008 1568309 0.0819 0.27424 0 1y_2009 Dummy for loans made in 2009 1568309 0.0811 0.27293 0 1

* *The matching market credit yield (spread): A1/P2 CP rate (minus 3-Month Treasury) if time to re-pricing less than one year and rating of 1,2A2/P2 CP rate (minus 3-Month Treasury) if time to re-pricing less than one year and rating of 3,4,5AAA bond rate (minus 10-Year Treasury) if time to re-pricing greater than one year and rating of 1,2BAA bond rate (minus 10-Year Treasury) if time to re-pricing greater than one year and rating of 3,4,5

44

Figure 1a. Distribution of prime rates charged by banks

Figure 1b. Choice of base rates across loan size categories

0

2

4

6

8

10

12

14

16

1997

q119

97q3

1998

q119

98q3

1999

q119

99q3

2000

q120

00q3

2001

q120

01q3

2002

q120

02q3

2003

q120

03q3

2004

q120

04q3

2005

q120

05q3

2006

q120

06q3

2007

q120

07q3

2008

q120

08q3

2009

q120

09q3

2010

q1

%

Prime Rate (FRB H.15) Average Prime Rate (STBL)

Max Prime Rate (STBL) Min Prime Rate (STBL)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

Prime rate Fed funds Domestic MM Foreing MM (LIBOR)

Other

Large Loans

Small Loans

45

Table 2. Regression analysis of C&I loan yields (1) (2) (3)

Explanatory variable - yield of loan interest rate All Loans New Loans Only New + Informal LCVARIABLES (1998Q1-2010Q1) (1998Q1-2010Q1) (1998Q2-2010Q1)

Dummy for loans < $100K 0.832*** 1.620*** 1.128***[0.173] [0.331] [0.269]

Dummy for loans in [$100K, $250K] 0.295** 0.915** -0.0128[0.124] [0.395] [0.445]

Dummy for loans in [$250K, $1M] 0.628*** -0.152 0.751**[0.0948] [0.240] [0.301]

Liquidity ratio -0.0565 0.216 0.286[0.395] [0.684] [0.663]

ROA 0.638 -1.237 6.448[2.726] [3.799] [6.454]

Capital ratio 2.914** 3.467 3.485*[1.216] [2.164] [1.870]

Asset size (normalized) -15.300 15.02 7.865[11.09] [29.74] [29.34]

NPL ratio 0.298 5.501 3.719[1.919] [4.102] [4.412]

Dummy for rating 2 0.488*** 0.713*** 0.676***[0.0651] [0.122] [0.109]

Dummy for rating 3 0.984*** 1.231*** 1.190***[0.0697] [0.139] [0.125]

Dummy for rating 4 1.301*** 1.608*** 1.539***[0.0703] [0.147] [0.131]

Dummy for rating 5 1.781*** 2.183*** 1.828***[0.0796] [0.150] [0.216]

Dummy for f loating-rate loans -0.0839* -0.166*** -0.195***[0.0446] [0.0566] [0.0552]

Dummy for secured loans 0.142*** 0.053 0.000762[0.0263] [0.0476] [0.0564]

Maturity 2.51e-05* -0.0000224 -0.0000234[1.28e-05] [1.97e-05] [1.69e-05]

Reference market yield 0.0452*** 0.0436** 0.0485***[0.00832] [0.0193] [0.0142]

Constant 6.291*** 3.357*** 3.928***[0.321] [0.497] [0.520]

Observations 914777 88703 112198N clusters 1086 811 860Adjusted R-sq 0.776 0.686 0.698P-value all Size1xTime Dummies = 0 for 2001 0.011 0.003 0.033P-value all Size2xTime Dummies = 0 for 2001 0.000 0.197 0.013P-value all Size3xTime Dummies = 0 for 2001 0.805 0.000 0.546P-value all Size1xTime Dummies = 0 for 2008-2009 0.187 0.011 0.997P-value all Size2xTime Dummies = 0 for 2008-2009 0.012 0.006 0.122P-value all Size3xTime Dummies = 0 for 2008-2009 0.001 0.000 0.118P value for cumulative effect Size 1 for 2001 0.004 0.456 0.000P value for cumulative effect Size 2 for 2001 0.484 0.422 0.013P value for cumulative effect Size 3 for 2001 0.000 0.000 0.240P value for cumulative effect Size 1 for 2008-2009 0.785 0.652 0.151P value for cumulative effect Size 2 for 2008-2009 0.192 0.775 0.227P value for cumulative effect Size 3 for 2008-2009 0.003 0.004 0.010

46

Figure 2a. Coefficient estimates on quarter dummies and interaction between quarter and small-loan size category dummies: All loans

47

Figure 2b. Coefficient estimates on quarter dummies and interaction between quarter and small-loan size category dummies: New term loans only

48

Table 3. Regression analysis of C&I loan spreads: prime-based loans only (1) (2) (3)

Explanatory variable - spread of loan interest rate All Loans New Loans Only New + Informal LCVARIABLES (1998Q1-2010Q1) (1998Q1-2010Q1) (2003Q2-2010Q1)

Dummy for loans < $100K 0.480** 1.942*** 1.127***[0.197] [0.186] [0.296]

Dummy for loans in [$100K, $250K] 0.434*** 1.670*** 0.571[0.134] [0.240] [0.472]

Dummy for loans in [$250K, $1M] 0.701*** 0.008 -0.285[0.103] [0.272] [0.303]

Liquidity ratio -0.182 0.6 0.128[0.397] [0.646] [0.787]

ROA 2.182 -2.969 5.889[2.609] [5.850] [11.06]

Capital ratio 4.261*** 5.374* 5.476**[1.450] [2.965] [2.741]

Asset size (normalized) -0.867 42.41 32.66[9.072] [29.98] [28.39]

NPL ratio 3.191* 13.15** 9.528[1.751] [5.578] [6.909]

Dummy for rating 2 0.548*** 0.696*** 0.722***[0.0758] [0.114] [0.114]

Dummy for rating 3 1.189*** 1.272*** 1.320***[0.109] [0.178] [0.181]

Dummy for rating 4 1.489*** 1.713*** 1.740***[0.111] [0.201] [0.194]

Dummy for rating 5 1.966*** 2.236*** 2.052***[0.114] [0.190] [0.208]

Dummy for f loating-rate loans -0.147*** -0.196*** -0.203***[0.0447] [0.0592] [0.0551]

Dummy for secured loans 0.0736*** 0.000 -0.0236[0.0249] [0.0553] [0.0575]

Maturity 8.76e-05*** 0.0000868 0.0000662[2.36e-05] [5.77e-05] [4.83e-05]

Reference market spread -0.166*** -0.0109 -0.0438[0.0581] [0.115] [0.115]

Constant -0.355 -3.055*** -0.758[0.375] [0.422] [0.596]

Observations 907404 88065 111082N clusters 1074 801 849Adjusted R-sq 0.412 0.493 0.486P-value all Size1xTime Dummies = 0 for 2001 0.967 0.006 0.682P-value all Size2xTime Dummies = 0 for 2001 0.124 0.001 0.487P-value all Size3xTime Dummies = 0 for 2001 0.000 0.521 0.201P-value all Size1xTime Dummies = 0 for 2008-2009 0.079 0.003 0.611P-value all Size2xTime Dummies = 0 for 2008-2009 0.002 0.001 0.778P-value all Size3xTime Dummies = 0 for 2008-2009 0.000 0.022 0.005P value for cumulative effect Size 1 for 2001 0.518 0.000 0.143P value for cumulative effect Size 2 for 2001 0.021 0.000 0.042P value for cumulative effect Size 3 for 2001 0.000 0.267 0.178P value for cumulative effect Size 1 for 2008-2009 0.049 0.000 0.103P value for cumulative effect Size 2 for 2008-2009 0.681 0.000 0.239P value for cumulative effect Size 3 for 2008-2009 0.002 0.000 0.093

49

Figure 3a. Coefficient estimates on quarter dummies and interaction between quarter and small-loan size category dummies: Spread regression; All prime-based loans

50

Figure 3b. Coefficient estimates on quarter dummies and interaction between quarter and small-loan size category dummies: Spread regression; New prime-based term loans only

51

Table 4. Regression analysis of C&I loan maturities (1) (2) (3)

Explanatory variable - maturity of the loan All Loans New Loans Only New + Informal LCVARIABLES (1998Q1-2010Q1) (1998Q1-2010Q1) (1998Q2-2010Q1)

Dummy for loans < $100K -89.39 -110.8 -41.29[79.42] [173.9] [158.0]

Dummy for loans in [$100K, $250K] -59.67 -111.8 159.9[81.89] [224.1] [335.9]

Dummy for loans in [$250K, $1M] 52.98 -253.6** 242.5[110.9] [128.9] [160.2]

Liquidity ratio -32.62 324.8 264.1[135.8] [273.6] [278.1]

ROA 522.2 1216 3704*[797.3] [1750] [2027]

Capital ratio -393.4 -2135** -1368[529.1] [1028] [1007]

Asset size (normalized) 1254 -1447 6824[4054] [9881] [11188]

NPL ratio 298.6 -2917 -2879[783.2] [2205] [1800]

Dummy for rating 2 48.02* 0.871 26.04[28.24] [63.48] [59.49]

Dummy for rating 3 -101.8*** -236.5*** -179.5***[27.42] [71.03] [62.92]

Dummy for rating 4 -97.08*** -75.86 -82.52[31.05] [133.1] [107.0]

Dummy for rating 5 -164.6*** -252.4*** -183.0***[28.84] [72.84] [69.22]

Dummy for f loating-rate loans 15.99 246.7*** 174.9***[31.56] [61.51] [54.99]

Dummy for secured loans 126.0*** 274.4*** 272.7***[15.75] [34.83] [32.19]

Reference market yield 230.1*** 298.9*** 276.5***[9.366] [21.34] [18.39]

Constant -791.3*** -1106*** -409.1*[135.5] [249.0] [232.4]

Observations 914777 88703 112198N clusters 1086 811 860Adjusted R-sq 0.338 0.403 0.371P-value all Size1xTime Dummies = 0 for 2001 0.566 0.016 0.029P-value all Size2xTime Dummies = 0 for 2001 0.976 0.449 0.726P-value all Size3xTime Dummies = 0 for 2001 0.709 0.010 0.019P-value all Size1xTime Dummies = 0 for 2008-2009 0.386 0.359 0.435P-value all Size2xTime Dummies = 0 for 2008-2009 0.382 0.248 0.060P-value all Size3xTime Dummies = 0 for 2008-2009 0.532 0.264 0.010P value for cumulative effect Size 1 for 2001 0.982 0.316 0.396P value for cumulative effect Size 2 for 2001 0.695 0.761 0.492P value for cumulative effect Size 3 for 2001 0.969 0.109 0.557P value for cumulative effect Size 1 for 2008-2009 0.359 0.488 0.114P value for cumulative effect Size 2 for 2008-2009 0.939 0.468 0.510P value for cumulative effect Size 3 for 2008-2009 0.365 0.077 0.007

52

Table 5. Regression analysis of C&I loan collateral status

(1) (2) (3)Explanatory variable - collateralization of the loan All Loans New Loans Only New + Informal LCVARIABLES (1998Q1-2010Q1) (1998Q1-2010Q1) (1998Q1-2010Q1)

Dummy for loans < $100K 1.069*** 0.236 0.108[0.172] [0.328] [0.285]

Dummy for loans in [$100K, $250K] 0.462*** 0.0136 0.0506[0.138] [0.611] [0.500]

Dummy for loans in [$250K, $1M] 0.256* 0.625*** 0.496**[0.144] [0.215] [0.213]

Liquidity ratio -0.759*** -0.403 -0.501**[0.218] [0.251] [0.244]

ROA 6.871 3.667 0.31[6.265] [6.368] [7.220]

Capital ratio 3.464*** -3.099 -2.990*[1.192] [1.919] [1.715]

Asset size (normalized) -3.729** -12.91*** -12.54***[1.505] [1.897] [1.602]

NPL ratio 6.410** 3.027 6.383[3.249] [4.268] [4.650]

Dummy for rating 2 -0.094 -0.11 -0.0852[0.103] [0.148] [0.124]

Dummy for rating 3 -0.275*** -0.157 -0.108[0.0941] [0.115] [0.123]

Dummy for rating 4 -0.155** -0.191* 0.0708[0.0757] [0.110] [0.122]

Dummy for rating 5 0.0565 0.0195 0.213[0.0698] [0.0982] [0.165]

Dummy for f loating-rate loans -0.041 -0.170** -0.153**[0.0488] [0.0771] [0.0692]

Maturity 0.000132*** 0.000278*** 0.000274***[2.01e-05] [3.72e-05] [3.39e-05]

Reference market yield -0.0185 0.0592*** 0.0437***[0.0120] [0.0176] [0.0146]

Constant -0.0118 0.992** 1.113***[0.320] [0.402] [0.351]

Observations 914777 88703 112198N clusters 1086 811 860Adjusted R-sq 0.070 0.135 0.122P-value all Size1xTime Dummies = 0 for 2001 0.654 0.278 0.085P-value all Size2xTime Dummies = 0 for 2001 0.001 0.470 0.008P-value all Size3xTime Dummies = 0 for 2001 0.061 0.106 0.046P-value all Size1xTime Dummies = 0 for 2008-2009 0.032 0.998 0.716P-value all Size2xTime Dummies = 0 for 2008-2009 0.311 0.023 0.769P-value all Size3xTime Dummies = 0 for 2008-2009 0.601 0.326 0.271P value for cumulative effect Size 1 for 2001 0.973 0.046 0.010P value for cumulative effect Size 2 for 2001 0.000 0.326 0.007P value for cumulative effect Size 3 for 2001 0.005 0.135 0.046P value for cumulative effect Size 1 for 2008-2009 0.050 0.654 0.453P value for cumulative effect Size 2 for 2008-2009 0.911 0.022 0.290P value for cumulative effect Size 3 for 2008-2009 0.808 0.965 0.821

53

Table 5a. Marginal effects of the size-quarter dummy interactions on the probability of collateral for the recession years: All Loans SMB_1 Delta-method SMB_2 Delta-method SMB_3 Delta-method

dy/dx Std. Err. [95% Conf. Interval] dy/dx Std. Err. [95% Conf. Interval] dy/dx Std. Err. [95% Conf. Interval]

2001Q1 0.031 0.003 0.026 0.037 2001Q1 0.188 0.002 0.184 0.193 2001Q1 0.118 0.002 0.114 0.1222001Q2 -0.010 0.003 -0.016 -0.004 2001Q2 0.167 0.002 0.162 0.171 2001Q2 0.130 0.002 0.126 0.1332001Q3 -0.013 0.003 -0.018 -0.007 2001Q3 0.115 0.003 0.110 0.120 2001Q3 0.117 0.002 0.112 0.1212001Q4 -0.015 0.003 -0.022 -0.009 2001Q4 0.154 0.003 0.148 0.160 2001Q4 0.108 0.003 0.103 0.113

SMB_1 Delta-method SMB_2 Delta-method SMB_2 Delta-methoddy/dx Std. Err. [95% Conf. Interval] dy/dx Std. Err. [95% Conf. Interval] dy/dx Std. Err. [95% Conf. Interval]

2008Q1 -0.059 0.003 -0.064 -0.123 2008Q1 0.046 0.002 0.042 0.084 2008Q1 0.037 0.003 0.031 0.0642008Q2 -0.073 0.003 -0.078 -0.151 2008Q2 0.016 0.002 0.011 0.023 2008Q2 0.012 0.002 0.008 0.0182008Q3 -0.123 0.003 -0.128 -0.249 2008Q3 -0.009 0.003 -0.015 -0.026 2008Q3 -0.024 0.003 -0.029 -0.0542008Q4 -0.054 0.003 -0.060 -0.114 2008Q4 0.045 0.003 0.039 0.080 2008Q4 -0.009 0.002 -0.013 -0.0242009Q1 -0.132 0.004 -0.139 -0.269 2009Q1 -0.042 0.003 -0.049 -0.093 2009Q1 -0.043 0.003 -0.050 -0.0942009Q2 -0.097 0.003 -0.102 -0.198 2009Q2 -0.008 0.003 -0.015 -0.025 2009Q2 -0.040 0.003 -0.045 -0.0862009Q3 -0.069 0.003 -0.074 -0.142 2009Q3 0.016 0.003 0.010 0.023 2009Q3 -0.003 0.003 -0.009 -0.0142009Q4 -0.089 0.003 -0.094 -0.182 2009Q4 -0.026 0.002 -0.030 -0.057 2009Q4 -0.007 0.003 -0.012 -0.021

54

Table 5b. Marginal effects of the size-time dummy interactions on the probability of collateral for the recession years: New loans only SMB_1 Delta-method SMB_2 Delta-method SMB_3 Delta-method

dy/dx Std. Err. [95% Conf. Interval] dy/dx Std. Err. [95% Conf. Interval] dy/dx Std. Err. [95% Conf. Interval]

2001Q1 0.031 0.052 -0.071 0.134 2001Q1 0.188 0.047 0.096 0.281 2001Q1 -0.033 0.013 -0.057 -0.0082001Q2 -0.010 0.053 -0.115 0.094 2001Q2 0.167 0.047 0.074 0.259 2001Q2 0.132 0.007 0.119 0.1452001Q3 -0.013 0.052 -0.115 0.090 2001Q3 0.115 0.052 0.012 0.218 2001Q3 0.180 0.007 0.167 0.1932001Q4 -0.015 0.057 -0.128 0.097 2001Q4 0.154 0.057 0.042 0.266 2001Q4 0.127 0.007 0.114 0.141

SMB_1 Delta-method SMB_2 Delta-method SMB_3 Delta-methoddy/dx Std. Err. [95% Conf. Interval] dy/dx Std. Err. [95% Conf. Interval] dy/dx Std. Err. [95% Conf. Interval]

2008Q1 0.009 0.008 -0.006 0.025 2008Q1 0.076 0.027 0.023 0.072 2008Q1 0.087 0.009 0.070 0.1042008Q2 0.037 0.007 0.023 0.051 2008Q2 0.123 0.034 0.056 0.144 2008Q2 0.048 0.011 0.026 0.0712008Q3 0.041 0.007 0.027 0.055 2008Q3 0.207 0.025 0.158 0.335 2008Q3 0.044 0.011 0.022 0.0652008Q4 0.036 0.011 0.015 0.058 2008Q4 0.259 0.026 0.208 0.434 2008Q4 -0.169 0.010 -0.190 -0.1492009Q1 0.044 0.017 0.011 0.078 2009Q1 0.123 0.035 0.054 0.141 2009Q1 -0.055 0.008 -0.070 -0.0402009Q2 0.068 0.018 0.033 0.104 2009Q2 0.137 0.029 0.080 0.186 2009Q2 -0.092 0.014 -0.120 -0.0642009Q3 0.050 0.013 0.024 0.075 2009Q3 0.216 0.040 0.138 0.310 2009Q3 0.008 0.011 -0.013 0.0292009Q4 0.015 0.013 -0.011 0.040 2009Q4 0.086 0.039 0.010 0.058 2009Q4 0.151 0.009 0.134 0.168

55

Table A.1. Description of regression variables Variable Description Data Source Variable Mnemonic(s)

Loan rate Effective Interest Rate STBL QTBL7961

Secured Dummy =1 if a collateralized loan STBL QTBL1929Maturity Maturity (in days) STBL QTBL9914

rating_1 Dummy for loans rated 1 STBL QTBLA344rating_2 Dummy for loans rated 2 STBL QTBLA344rating_3 Dummy for loans rated 3 STBL QTBLA344rating_4 Dummy for loans rated 4 STBL QTBLA344rating_5 Dummy for loans rated 5 STBL QTBLA344floating Dummy =1 if a loan has floating rate STBL QTBLA341comloan1 Dummy =1 if a loan made under a commitment STBL QTBL1915

xYield1 Market Debt security yields FRB H.15A1/P2 CP rate if maturity less than one year and rated 1,2 FRB H.15A2P2 CP rate if maturity less than one year and rated 3,4,5 FRB H.15AAA bond rate if maturity greater than one year and rated 1,2 FRB H.15BAA bond rate if maturity greater than one year and rated 3,4,5 FRB H.15

Treasury rate Linear Interpolated treasury rate of days to maturity FRB H.15xspread1 Market Debt Security Spreads FRB H.15

A1/P2 CP rate minus 3-Month Treasury if maturity less than one year and rating of 1,2 FRB H.15A2/P2 CP rate minus 3-Month Treasury if maturity less than one year and rating of 3,4,5 FRB H.15AAA bond rate minus 10-Year Treasury if maturity greater than one year and rating of 1,2 FRB H.15BAA bond rate minus 10-Year Treasury if maturity greater than one year and rating of 3,4,5 FRB H.15

Liquid ratio (cash+securities+trading assets)/assets Call Reports (RCFD0010+RCFD1754+RCFD1773+cash: rcfd0010; securities: rcfd1754+rcfd1773; trading assets: rcfd3545; assets: rcfd2170 +RDFD3545)/RCFD2170

ROA quarterly income/assets Call Reports RIAD4340/RCFD2170Capital ratio capital/assets Call Reports RCFD3210/RCFD2170Bank size share of bank assets = assets/aggregate banking sector assets Call ReportsNPL ratio non-performing loans/assets Call Reports (RCFD1403+RCFD1407)/RCFD2170