Risk Overhang and Loan Portfolio Decisions:

Small Business Loan Supply Before and During the Financial Crisis

CBE Research Paper #2014-1

Robert DeYoung, University of Kansas Anne Gron, NERA Economic Consulting

Gokhan Torna, State University of New York at Stony Brook Andrew Winton, University of Minnesota

This draft: April 22, 2014

Abstract: We find evidence that community banks restricted credit to small and medium sized enterprises in the U.S. during the global financial crisis. We estimate a structural model of bank portfolio lending with market imperfections, and exploit two sources of exogenous within-sample variation to identify our tests. Banks became less tolerant of risk during the crisis as loans became more difficult to sell and equity capital more expensive, resulting in pro-cyclical risk overhang effects. Our findings are consistent with crisis-era studies of European bank lending, but go further by showing that these behaviors can be explained by financial intermediation theory.

The opinions expressed in this paper do not necessarily reflect the views of NERA Economic Consulting. We thank Allen Berger, Lamont Black, Paolo Fulghieri, Ted Juhl, Greg Udell and seminar participants at Bangor University, the Bank of Canada, the Federal Deposit Insurance Corporation, the Federal Reserve Bank of Chicago, the University of Groningen, the University of Kansas and the University of Limoges for their insightful comments and suggestions.

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1. Introduction

Small businesses, defined as having less than 500 employees, employ about one-half of the U.S.

labor force and create nearly two-thirds of net new private sector jobs in the U.S. annually (U.S. Small

Business Administration, 2012). Virtually all of these small firms are privately held and lack access to

public capital markets. To ensure access to credit, these informationally opaque businesses establish close

borrower-lender relationships with small, so-called ‘community banks’ (e.g., Petersen and Rajan 1994;

Berger, Saunders, Scalise, and Udell 1997; Berger, Miller, Petersen, Rajan and Stein 2005). This

confluence of small firms and small banks is uniquely important for macro-economic growth both in the

U.S. and elsewhere: Berger, Hasan, and Klapper (2004) found a strong positive link between a large, healthy

small banking sector and macro-economic growth across 49 developed and developing nations.

The financial crisis took a toll on the U.S. small banking sector. About 6% of for-profit depository

institutions (commercial banks and thrift institutions) failed between 2007 and 2012, and 411 of those 478

insolvencies were small institutions with assets less than $1 billion (http://www.fdic.gov). It is

understandable that small business clients of these failed institutions would suffer interruptions, reductions

or even outright loss of their credit lines as the FDIC fashioned resolutions for these banks.1 But it remains

an open question whether the stress of the financial crisis caused healthy banks in the U.S. to reduce the

amount of new credit they supplied to small and medium enterprises (SMEs). A reduction in SME credit

supply by healthy banks—that is, a credit crunch or credit rationing—would have pro-cyclical effects,

exacerbating the economic downturn by denying firms the short-term credit necessary to finance increased

inventories and retain workers. Moreover, credit rationing by small banks would be antithetical to the

whole idea of a banking relationship, which carries with it the presumption that additional credit will be

available when needed. In this paper, we investigate whether, how and why small U.S. banks reduced their

supply of credit to small businesses during the financial crisis.

1 The FDIC arranged ‘purchase and assumption’ resolutions for 427 of these failed banks. In these transactions, the FDIC arranges for a healthy bank to acquire all of the assets of the failed bank, so clients of these failed bank were unlikely to fully lose access to credit. In the other 51 bank insolvencies, the FDIC seized the failed bank’s assets and disposed of them piecemeal over time; clients of these banks were more likely to fully lose access to new credit.

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Some evidence has emerged—mainly from European economies where credit registries provide

researchers with highly detailed data on loans and loan applications—that the financial crisis was

accompanied by reduced credit supply to SMEs (e.g., Popov and Udell 2010; Cotugno, Monferra and

Sampagnaro 2012; Jimenéz, et al 2012). These studies document that credit supply declined more during

the crisis at banks experiencing financial stress (low levels of equity capital, poorly performing loan

portfolios) but declined relatively less for SMEs with strong bank-borrower relationships. While this body

of research is informative and in some cases impressive, it remains incomplete. First, none of the extant

research examines credit to U.S. small businesses. By necessity, U.S. research has focused on the

syndicated loan supply to large firms during the crisis (e.g., Ivashina and Scharfstein 2010a, 2010b) because

systematic loan-level data for SMEs are not available. Given that the business, banking and financial

environments in the U.S. and Europe are substantially different, one cannot simply assume that small

business credit supply behaved similarly on both sides of the Atlantic. Second, the extant studies employ

pure empirical methodologies and ad hoc econometric test specifications. While these studies find well-

identified statistical associations between financial conditions and SME credit supply, they leave un-

modeled and unexplained the behavioral phenomena that drive these empirical associations and the

channels through which these associations occur. In order to successfully prevent credit supply

inefficiencies during recessions, policymakers need to know not just whether the actions of small business

lenders help perpetuate the downturn, but more importantly why and how this pro-cyclical behavior occurs.

We address both of these shortcomings in the extant literature, using data from small U.S. commercial

banks to estimate a structural econometric model of loan supply to small business firms.

We estimate a small business loan supply model for U.S. commercial banks both before and during

the financial crisis. Because loan-level data for SME loans are not systematically available in the U.S., we

use lender-level data from small U.S. commercial banks. These banks are not large enough to make or

even participate in loans to large firms; all of their new business loan originations, as well as all of their

business loans held in portfolio, are SME loans. Having limited our sample in this way, the observed

quarter-to-quarter change in bank-level business loans become a natural measure of net new SME loan

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supply. We base our empirical loan supply equation closely on the theoretical loan supply function, which

we derive from a bank loan portfolio model in which market imperfections (illiquid loans, costly external

capital) make bank lenders effectively risk averse (Froot, Scharfstein and Stein, 1993; Froot and Stein,

1998). Thus, in the course of testing empirically whether U.S. banks reduced and/or rationed credit to

SMEs during the global financial crisis, we also perform an important empirical test of financial

intermediation theory.

Froot, Scharfstein and Stein (1993) predict that, when external finance is costly, value-maximizing

firms make investment decisions in a risk-averse manner: they base decisions not only on the expected

returns from the investment opportunity in question, but also on their stock of available investment capital

and the new investment’s return covariance with the rest of their business. These considerations increase

a firm’s expected profits by reducing the probability that it will forego a valuable future investment

opportunity when the return on the prospective investment does not justify the costs of raising additional

external capital—either because the firm has too little internal capital to make the investment or it is unable

to free-up internal capital by selling off lower yielding assets because they are illiquid.

Froot and Stein (1998) apply this theory to banks. In their role as delegated monitors, banks have

private information that makes their loans relatively or completely illiquid, which leads to the central

implications of our theory model: if existing loans are illiquid and cannot be cheaply sold off, and if the

returns on these existing exposures positively covary with the returns on business loans, then capital

constrained banks will make fewer new business loans. Similarly, if a bank with largely illiquid existing

loans suffers a reduction in its equity capital, then the bank will also make fewer new illiquid loans. We

refer to these phenomena as ‘risk overhang’ or ‘loan overhang’ effects (Gron and Winton 2001). These

effects should grow stronger during economic downturns—during which preexisting loans become both

riskier and more illiquid, and equity capital both shrinks and becomes more costly—and as a result bank

lenders will become effectively more risk averse. Should we find that small banks did reduce their supply

of credit to SMEs during the financial crisis, then our theory provides several testable hypotheses about the

motivations for doing so and the channels through which it was done.

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The assumptions upon which we base our theory model are especially appropriate for SME lending

by small banks. SME loans are illiquid assets and must be held in portfolio where they lock up equity

capital. Small banks are seldom publicly traded, rarely have public credit ratings, and face relatively

inelastic deposit markets,2 all of which make external capital expensive. Small bank shareholders tend to

be poorly diversified—ownership is often concentrated within a single extended family, with a

disproportionate share of owners’ wealth invested in the bank (Spong and Sullivan 2007)—which further

encourages risk-averse business practices. Likewise, the financial crisis provides a natural environment for

testing the predictions of our theory model: bank equity capital became more costly, financial markets

became less liquid, and (casual empiricism suggests) lenders became more risk averse.

We test the loan supply predictions of our model for a panel of quarterly data on U.S. banks with

assets less than $2 billion (2010 dollars) operating in metropolitan and urban markets between 1991 and

2010. We use a standard 2SLS-IV estimation approach—with bank fixed effects, time fixed effects, and

theoretically consistent economic conditions variables to absorb variation in local loan demand—to account

for the simultaneity of banks’ new SME loan supply decisions with their new lending decisions in other

loan sectors (consumer loans, real estate loans). We gain identification by embedding two separate

difference-in-differences frameworks into the empirical supply equation, which we specify using

exogenous variation in the market imperfections central to our model: exogenous bank-specific differences

in loan liquidity and exogenous bank-specific differences in the cost (availability) of external equity capital.

For our first source of exogenous variation we exploit differences in bank corporate organization

form. Banks organized as subchapter S corporations do not pay corporate income tax, but they are required

to regularly distribute a large portion of their net income to shareholders as dividends, where personal

income tax rates are then applied to the income. Moreover, tax law places an upper limit on the number of

shareholders in an S corporation. Hence, external capital is especially costly for subchapter S banks.

According to our theory, a shock to personal income tax rates in the home states of S corporation banks

2 For evidence that bank deposit markets are fairly inelastic, see Amel and Hannan (1999).

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should result in especially strong loan overhang effects. Our empirical tests confirm this expectation. For

our second source of exogenous variation we exploit differences in bank business strategies. At small

banks, loans to small companies (e.g., SME business loans, commercial real estate loans) are

informationally opaque and especially illiquid, but loans to households (e.g., consumer loans, mortgage

loans) are relatively less illiquid because these loans are often securitizable. Hence, the loan portfolios of

banks with long-established “commercial focused” lending strategies will be more illiquid than banks with

other business strategies. According to our theory, a shock to the cost or availability of external capital

(i.e., the onset of the financial crisis) should result in especially strong loan overhang effects at these banks.

Our empirical tests also confirm this expectation.

On average, our empirical results indicate that small U.S. banks reduced their supply of credit to

SMEs during the financial crisis. Moreover, these findings look like credit rationing: we find a strong

positive relationship between net new SME lending and the expected returns on SME loans prior to the

crisis, but after the onset of the crisis SME loan supply becomes insensitive (perfectly inelastic) on average

to expected loan returns. However, the small segment (about 13%) of the banks in our data with commercial

focused lending strategies supplied increased amounts of credit to small businesses during 2008 (the first

full year of the crisis) and then maintained this higher level of SME credit supply during both 2009 and

2010. These results imply that borrower-lender relationships help mitigate credit supply shocks to small

businesses, consistent with the findings of non-U.S. studies based on loan-level data (Cotugno, Monferra

and Sampagnaro 2012 for Italian banks; Liberti and Sturgess 2012 for a single multinational lender).

Our results are largely consistent with the predictions of our theory. We find strong evidence of

loan overhang effects. All else equal, banks make fewer new business loans when their portfolios contain

large amounts of preexisting business loans, and make more new business loans when their portfolios

contain large amounts of loans to other sectors (e.g., consumer loans) that covary negatively with business

loans. These loan overhang effects grew stronger during the financial crisis, consistent with reductions in

loan liquidity and lender risk tolerance during an economic downturn. We also find strong evidence

consistent with the theoretical ‘risk tolerance’ predicted by our model, in which the new supply of illiquid

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loans varies positively with fluctuations in a bank’s equity capital. Prior to the crisis, a decrease in a bank’s

equity capital cushion is associated with a reduction in new business loan supply. During the crisis, this

risk-averse lending behavior continues for well-capitalized banks, but it disappears for banks with less

equity capital. While the latter result is consistent with the literature on risk-seeking behavior at poorly

capitalized banks (Merton 1977, Marcus 1984), it may simply indicate that rebuilding their equity capital

bases was the paramount objective for poorly capitalized banks during the crisis, thus disconnecting for a

time their capital levels from their new lending decisions.3

While our results confirm the main findings of previous studies of small business lending during

the financial crisis—namely, that supply-side phenomena were important drivers of reduced credit

availability for SMEs—we also extend this body of knowledge in a number of ways. First, our econometric

methodology allows us to estimate the impact of the financial crisis on SME lending in the U.S., even in

the absence of loan-level data. Second, by using theory to inform these empirical tests, we are able to

empirically identify some of the meta-drivers of SME lender behavior, i.e., loan illiquidity, equity capital

supply and lender risk aversion. Third, we find that these determinants of SME loan supply vary in strength

across the business cycle, consistent with models of pro-cyclical bank lending driven by internal bank

behavior (e.g., Rajan, 1994; Berger and Udell, 2004; Ruckes, 2004; Repullo and Suarez, 2013). Risk

overhang effects are pro-cyclical: small business loan supply declines during economic downturns by even

more than would be implied by recessionary reductions in bank capital alone. When loan securitization

markets broke down during the financial crisis, banks were less able to sell their outstanding stocks of real

estate and consumer loans, and this increase in loan portfolio illiquidity tied up equity capital that could

otherwise have been used to back new small business lending. When declining stock market conditions

(lower prices, higher price volatility) made issuing new risk capital more expensive, banks became more

circumspect (effectively more risk averse) when allocating their existing risk capital, which exacerbated

3 Differentiating between these two possible explanations lies beyond the scope of this study.

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extant loan portfolio overhang effects and made banks less likely to extend new business credit at the

margin.

The plan of the paper is as follows. In Section 2 we review the previous research studies that are

most relevant for our investigation. In Section 3 we derive a theoretical loan supply function from a model

of bank loan portfolio allocation with capital market imperfections. In Section 4 we make some adjustments

to the theoretical loan supply equation to make it suitable for empirical estimation and hypothesis testing.

In Section 5 we show that community banks in the U.S. have characteristics that comply closely with the

maintained assumptions of our theory model, and as such provide a natural venue for testing its predictions

for SME loan supply. In Section 6 we present the data and variables used in our regression models. In

Section 7 we describe our empirical identification schemes. In Section 8 we present the results of our main

regression tests and robustness tests. In Section 9 we summarize our findings and discuss their implications

for policy.

2. Related literature

A large body of empirical studies investigate whether implementation of the Basel I capital

requirements caused a credit crunch in the U.S. (e.g., Bernanke and Lown 1991, Hall 1993, Haubrich and

Wachtel 1993, Berger and Udell 1994, Hancock and Wilcox 1993, Brinkman and Horvitz 1995, Peek and

Rosengren 1995). In general, these studies relate loan growth to capital measures and other controls.

Although this literature does not generate a consensus on the relationship between bank capital and loan

supply, Sharpe (1995) identifies two robust results across the studies: bank profitability has a positive effect

on loan growth, and loan losses have the opposite effect. Since profits (loan losses) tend to increase

(decrease) bank capital, these findings are consistent with a positive bank capital-loan growth link. In more

recent work, Beatty and Gron (2001) find that banks with stronger capital growth have greater loan growth,

with the most significant effects coming from the most capital-constrained banks.

The global financial crisis has motivated a new stream of studies on bank capital and bank loan

supply. Perotti, Ratnovski and Vlahu (2011) derive a non-monotonic theoretical relationship between bank

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capital and bank risk-taking. When banks are operating near their regulatory capital minimums, additional

capital results in fewer tail risk projects (consistent with a reduction in the value of the deposit put option,

e.g., Merton 1977, Marcus 1984). However, when capital is so high that banks have no worry of breaching

their regulatory capital minimums, additional capital results in more tail risk projects; hence, capital

supports risk tolerance. Empirical studies by Black and Hazelwood (2011), Duchin and Sosyura (2010)

and Li (2011) all find at least some evidence of increased lending (i.e., greater risk-taking) at banks that

received government capital injections, while Carlson, Shan and Warusawitharana (2011) find bank lending

during the financial crisis was most sensitive to increases in capital at banks with low capital ratios. These

findings have obvious policy implications; however, because they focus narrowly on bank lending behavior

in response to artificial (non-market) capital injections during a period of severe financial stress, they

provide an incomplete treatment of the bank capital-loan supply relationship.

Much of our current knowledge about the impact of the financial crisis on small business loan

markets comes from European economies, where credit registries provide researchers with highly detailed

data on loans and loan applications. Jimenéz, Ongena, Peydro and Saurina (2012) find that reductions in

business lending in Spain during the financial crisis were predominantly caused by supply-side effects due

to weak bank balance sheets, rather than demand-side forces. Popov and Udell (2010) find that both supply-

side and demand-side factors led to reduced SME lending in 14 European countries: banks experiencing

stress to their assets and equity values extended less credit, and high-risk SMEs with fewer tangible assets

received less credit, during the early stages of the financial crisis. Cotugno, Monferra and Sampagnaro

(2012) find that SMEs in Italy experienced reduced credit supply during the financial crisis, but that credit

rationing was substantially mitigated for loan applicants with exclusive borrowing relationships with their

banks.

Research on U.S. bank lending during this period tends to use data on large business lending.

Ivashina and Scharfstein (2010a, 2010b) show that shocks to bank liquidity (e.g., deposit withdrawals,

credit line draw downs) were associated with reduced lending to large corporate customers during the crisis.

Montorial-Garriga and Wang (2012) derive a model of bank loan pricing with endogenous credit rationing,

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and estimate it using a sample of U.S. bank loans during the 2000s; the authors conclude that large business

borrowers were less likely than small firms to be rationed out of the bank loan market during the financial

crisis. Garcia-Appendini and Montoriol-Garriga (2011) show that large, liquid firms provided increased

trade credit to their customers during the crisis, perhaps substituting for a reduction in credit supply from

banks.

Our study differs from the previous literature in several respects. First, while most previous studies

focused on large banks, we focus exclusively on small banks to ensure that the loan supply we are observing

is going to small businesses. Second, previous studies estimated reduced-form regression models, whereas

we estimate a structural econometric model based on a theory of loan supply that is highly descriptive of

the opportunities and constraints facing small bank lenders. Third, most previous studies used annual data

over a limited period of time, whereas we observe detailed changes in portfolio composition and loan supply

at quarterly intervals over 20 years. Observing data at these more frequent quarterly intervals is essential

for testing the loan portfolio hypotheses in our theory model. Fourth, within the small set of studies that

test the impact of the financial crisis on bank lending, we are the first to examine this question exclusively

for small business lending in the U.S. Finally, and perhaps crucially, we are able to empirically identify

the relationships between SME loan supply and bank balance sheet conditions and lending behavior (e.g.,

loan overhang, loan illiquidity, risk tolerance) without access to either loan-level data or a convenient

natural experiment.

Our work is rooted in the theoretical literature that models financial institution portfolio

management when external financing is costly due to capital market imperfections. These theories apply

particularly to banks with enough equity so that moral hazard via risk shifting does not become an issue.4

Froot, Scharfstein and Stein (1993) show that firms facing costly external finance, stochastic net worth, and

4 It is well-known that banks with very low capital levels may engage in moral hazard via risk-shifting, possibly by overly aggressive lending, as in Marcus (1984). This is more likely if deposit insurance is priced at a flat rate. By contrast, if capital levels are not very low, banks may become more conservative in their lending when capital levels fall, as in Besanko and Kanatas (1996), Thakor (1996), Holmstrom and Tirole (1997), Diamond and Rajan (2000) and Perotti, Ratnovski and Vlahu (2011).

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attractive future investment opportunities will behave in a risk-averse manner. Froot and Stein (1998)

extend this model to include the influence of preexisting portfolios of investments on financial institutions

new investment decisions. These authors show that the amount the institution will want to invest in a new

opportunity will depend upon its level of capital, the covariance of that investment’s cash flows with the

cash flows of the firm’s stock of illiquid (or non-tradable) asset exposures, and the covariance of the non-

tradable cash flows of any other new investments the firm is considering. Froot (2007) extends the

framework further in a model of insurance companies, introducing product market imperfections and

allowing some of the risks faced by insurers to be hedged. Several empirical applications of this framework

exist. Froot and O’Connell (1999) apply this model to price determination in the catastrophe reinsurance

market. They show that such financing imperfections can lead to costly reinsurer capital and also to

reinsurer market power, and estimate the corresponding supply and demand curves. Gron and Winton

(2001) use the term ‘risk overhang’ to describe how outstanding and illiquid risk exposure from long-term

insurance policies can affect the current supply of new insurance policies. In extreme cases, increases in

risk overhang may lead firms to reduce their total exposure to the underlying risk by canceling existing

policies.

3. Loan Supply with Capital Market Imperfections: Theory

In this section we develop a portfolio model of bank loan supply. We begin with a representative

bank which has lending opportunities in several sectors. Loans can be funded out of net internal capital W

or external funds F, where external funds are assumed to be more costly than internal funds. This additional

cost reflects information asymmetries between the firm and outside investors (e.g., Myers and Majluf 1984,

DeMarzo and Duffie 1999), as well as other transaction costs in accessing public markets. In addition to

current period loans, the bank may be able to make profitable loans in future periods. As shown by Froot,

Scharfstein and Stein (1993), profitable future investment opportunities combined with costly external

funds and stochastic internal funds cause the firm's objective function to be increasing and generally

concave in the stock of internal funds. Intuitively, more internal funds lessen the extent to which a bank

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must rely on costly external funds, but this benefit is generally decreasing because, at the margin, there are

fewer profitable uses for these funds. Denoting the indirect form of the bank's objective function as P(W),

we have PW > 0 and PWW < 0 where the subscript denotes the partial derivative.

The bank begins period t with Wt-1 in net internal funds, Lt-1,i in outstanding loans in each sector i,

and net external finance of Ft-1=∑i (Lt-1,i) -Wt-1 > 0. For simplicity, we assume that all external finance

takes the form of debt.5 For the moment, assume that all of the bank’s outstanding loans are illiquid and

cannot be sold due to the bank’s private information on loan quality. Since the bank must bear the risk of

Lt-1,i loans in each sector i regardless of its subsequent decisions in period t, Lt-1,i is the bank’s risk overhang

in sector i in period t.

During period t the bank can make new loans NLt,i ≥ 0 to each sector i, resulting in end-of-period

outstanding debt of Ft = ∑i (Lt-1,i+ NLt,i) - Wt-1. The gross per dollar cost of debt funding is 1+r t, which

includes any costs of accessing external markets rather than using internal capital. During period t, the

bank realizes the gross per dollar return of 1/,

~−titR on loans to sector i that were originated in period t-1.

1/,

~−titR equals 1+r t+pt-1,i-η~ t,i, where pt-1,i is the per dollar credit spread or markup charged on sector i loans

that originated in period t-1, and η~ ti is the random per dollar loan losses on sector i loans in period t.

Similarly, the bank realizes the gross per dollar return titR /,

~ = 1+r t+pt,i-η~ t,i on the new loans to sector i

originated in period t, where pt,i is the per dollar credit spread on these loans. For simplicity, we assume

5 Regardless of its form, external finance is costly for banks. In the presence of binding (or even close to binding) minimum regulatory capital requirements, banks must raise external debt in combination with new equity. Indeed, Berger, DeYoung, Flannery, Lee and Oztekin (2008) show that when commercial banks fall closer to their regulatory minimums, they actively manage their capital to return quickly to their internal capital targets. Issuing new equity involves significant transaction and informational costs, especially for banking companies that are not publicly traded (the majority of the industry). For banks that are not too-big-too-fail (again, the majority of the industry), issuing subordinated debt or large denomination deposit contracts also entails such costs. And although (non-TBTF) banks can issue federally insured retail deposits that would seem to be unaffected by such information concerns, there is evidence that these debt contracts are not perfect, costless substitutes for uninsured debt. Billett et al. (1998) find that large banks increase their use of insured deposits following downgrades of their publicly traded debt, but also find that total debt finance (insured plus uninsured liabilities) declines, consistent with increased external costs of debt finance. Further support that external funding is costly for banks comes from Jayaratne and Morgan (2000), who find that banks finance an unusually large portion of their assets with internal funds. Finally, Amel and Hannan (1999) show that markets for insured deposits are relatively price inelastic, indicating that banks cannot raise large additional amounts of these funds without significantly increasing the rate they pay.

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that all losses on loans to sector i borrowers in period t are perfectly correlated, regardless of when the loan

was made. Current period loan losses are assumed to be normally distributed: ),(~~,,, ititit N σµη where

both µt,i and σt,i depend on the sector’s economic outlook at the start of that period.6 Both µt,i and σt,i are

decreasing in the sector's economic outlook: when borrowing firms have better prospects, both ex ante

credit risk and ex post realized loan losses are lower because the borrowing firms’ chances of default are

reduced. Given these assumptions, it follows that the bank’s net capital at the end of period t is

)]~()~([)1(

)1(]~~

[~

,,,1

,,1,10

/,,1

1/,,1

ititit

n

iitititt

tttitit

n

itititt

pNLpLrW

rFRNLRLW

ηη −+−++=

+−+=

∑

∑

=−−

=−−

(1)

where we have made use of the definitions of 1/,

~−titR , titR /,

~, and Ft.

The bank chooses new loan amounts NLt,i that maximize expected profit E[P( tW~

)], given the

financing constraints. This leads to the first order condition for each sector i

)~,()]([)]~([]~

[0 ,,,,,,

itWititWititWit

tW PCovpPEpPE

NL

WPE ηµη −−=−=

∂∂= , (2)

where we have made use of (1) and the identity E(xy) = E(x)E(y) + Cov(x,y). Since loan losses it ,~η and

the level of internal funds tW~

are both normally distributed, we can apply Stein’s Lemma and the definition

of covariance to derive the bank’s supply of new loans SitNL , to sector i 7

.1 ,,

,1,1,,ii

itit

ii

ij

ij jtitii

ijSjtij

Sit

p

GLLNLNL

σµ

σσ

σσ −

⋅+−−−= ∑∑ ≠ −−≠ (3)

where for convenience we have suppressed the time subscript on the loan performance variance and

6 In reality, loan losses are skewed to the right: they cannot be less than zero, there is a high probability that they won’t be too large, and a low probability of very large losses. The assumption of normality allows us to give a simple, tractable analytic solution to the bank’s portfolio choice problem. 7 Stein’s lemma implies Cov(PW, it ,

~η ) = E[PWW]Cov( tW~

, it ,~η ). We also use Cov(tW

~, it ,~η ) =

ji)σj jtNLjt(L ,,,1∑ +−− .

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covariance terms. In (3), σii is the variance of loan losses in sector i over time; σij is the covariance of loan

losses across sectors i and j over time; ][

][

W

WW

PE

PEG −= measures the bank’s effective risk aversion induced

by the costs of external finance, and hence we shall refer to its reciprocal 1/G as the bank’s risk tolerance.

The bank’s supply of new loans to sector i is determined by several factors on the right-hand side

of equation (3). The first term is the effect of covariance-adjusted lending opportunities in other sectors j≠i

at time t. The second term is the preexisting portfolio exposure in sector i, that is, the overhang of

outstanding loans in sector i at time t. The third term is the effect of the covariance-adjusted loan overhangs

in other sectors j≠i. The final term is the bank’s tolerance 1/G multiplied by the risk-adjusted profit ratio

(pt,i-µt,i)/σii. It is straightforward to verify that equation (3) has the features of a supply curve. The supply

of new loans to sector i is increasing in the current credit spread (or ‘markup’) pt,i and decreasing in expected

loan losses (or costs) µi,t. Assuming that pt,i exceeds µt,i, new loan supply is also decreasing in the bank’s

effective risk aversion G. Further, the supply of new loans to sector i is decreasing in the overhang of

outstanding loans in that sector, Lt-1,i. Finally, if the covariance between sector i and sector j is positive,

then the supply of new loans in sector i is decreasing in both the overhang of outstanding loans in sector j

and the supply of new loans in sector j; by contrast, if the covariance is negative, then the supply of new

loans in sector i is increasing in loans to sector j.

4. Loan Supply with Capital Market Imperfections: Issues for Empirical Specification

Equation (3) forms the basis for our empirical analysis. Before estimating this model, we must

make adjustments for two features of the banking data that are not perfectly consistent with the theoretical

assumptions above: some bank loans are not perfectly illiquid, and new loan supply is not directly

observable.

4.1. Banks hold liquid and illiquid loan stocks

During a given accounting period, some loans will mature and be repaid. The remaining loan stocks

exhibit varying degrees of liquidity. As shown by Froot and Stein (1998), under optimal portfolio allocation

14

with imperfect capital markets, it is optimal for banks to shed all loans that can be sold at fair value.

However, due to information asymmetries or transactions costs, the market prices of loans may be less than

banks’ expected values, resulting in illiquid loans which banks hold rather than sell.

Let δt-1,i ∈(0,1) be the illiquid portion of the outstanding loans at the beginning of period t (end of

period t-1). The remaining loans are assumed to be liquid and will be sold off at no cost, or will run off

naturally, to make room for new loans. Since only illiquid loan stocks will affect new lending, we can

rewrite equation (3) as

ii

itit

ii

ijij jtjtitit

ii

ijSjtij

Sit

p

GLLNLNL

σµ

σσ

δδσσ ,,

,1,1,1,1,,

1 −⋅+∑−−∑−= ≠ −−−−≠ (3′)

where we have substituted the illiquid stock of outstanding loans δt-1,iLt-1,i and δt-1,jLt-1,j in place of the total

(liquid and illiquid) stock of outstanding loans Lt-1,i and Lt-1,j. Unfortunately, while equation (3') is the

theoretically correct relationship, we cannot observe the fractions δt-1,i and δt-1,j in the available banking data.

Thus, although the theoretical equation (3') predicts that the coefficient on the outstanding (illiquid) same-

sector loan stock variable (δt-1,iLt-1,i) will be exactly -1 (that is, every dollar of illiquid loans causes the bank

to forgo one dollar of new loans), in our regressions the estimated coefficient on the total outstanding same-

sector loan stock variable (Lt-1,i) will simply absorb the theoretical illiquidity term δt-1,i. Thus, we would

expect the estimated regression coefficients on Lt-1,i and Lt-1,j to be larger (i.e., closer to 1 in absolute value)

as these outstanding loan stocks become more illiquid.

The degree to which outstanding loans are liquid or illiquid is not fixed but can change with

exogenous conditions. For example, a recession may reduce the liquidity of outstanding loans: borrowers

will be more likely to roll over rather than repay drawn down credit, and increased adverse selection

problems make it more costly for banks to sell or securitize loans. Additionally, a recession may have a

capital effect: with the expectation of increased future losses on outstanding loans—and thus lower equity

capital levels in the future—banks will become more risk averse lenders.

4.2. New loans are unobservable

The new loan supply NLS is not directly observable in the data; we only observe the outstanding

15

stock of loans at the end of each accounting period. Hence, we calculate the quarter-to-quarter net lending

change NLC = Lt,i - Lt-1,i and use this to proxy for NLS. Note that the stock of outstanding sector i loans Lt,i

at the end of period t is the sum of three items: the illiquid portion of the period t-1 loan stock, any retained

liquid portion of the period t-1 loan stock, and the new period t loans. Letting τt,i ∈(0,1) represent the

fraction of outstanding liquid sector i loans from period t-1 that the bank retains at the end of period t, it

follows that Lt,i equals (δt,i + τt,i(1-δt,i))Lt-1,i + NLSt,i. Thus, we have

itititS

it

itititititS

it

ititit

LNL

LLNL

LLNLC

,1,,,

,1,1,,,,

,1,,

)]1)(1[(

)]1([

−

−−

−

−−−=

−−++=

−=

δτ

δτδ

which shows that measured NLC equals the actual supply of new loans less the portion of liquid loan stocks

that are actually sold. In practice, banks will sell some liquid loans if they can do so at fair prices, or will

hold some liquid loans for strategic purposes. As either the portion of loans that are illiquid (δ) or the

portion of liquid loans that are retained (τ) increase—conditions that are more characteristic of small banks

than of large banks—then NLC becomes more highly correlated with new loan supply NLS.

4.3. Empirical loan supply model

We make several additional adjustments to transform the theoretical loan supply equation (3′) into

an estimable business loan supply equation:

11

11

1,1,1

3,2,11,11

3,2,1,

−

=−−−

=+

−+∑−∑−= t

tt

iitit

iitit G

pLLNLCNLC ξ

σµ

χρβφ (4)

where the subscript i indexes each of the three loan sectors in our data (business = 1; real estate = 2;

consumer = 3) and t indexes time in quarters. As previously discussed, the loan stock variables Lt-1 measure

total preexisting loans (not just the illiquid portions δt-1Lt-1) and the net lending change NLCt variable proxies

for unobservable new loan supply NLtS. We specify bank risk tolerance G-1 and risk-adjusted loan return

(pt,i-µt,i)/σii linearly rather than multiplicatively in order to estimate the independent effects of these

16

measures.8 The regression coefficients φ, β, ρ, χ and ξ are parameters to be estimated. The coefficients φ

and ρ absorb (and hence will reflect) the effects of the suppressed covariance-variance ratios σij/σii while

the coefficients β and ρ absorb (and hence will reflect) the unobserved liquidity effects δt and τt as discussed

above.

In our estimations, we additionally control for fixed bank effects, fixed time effects, and economic

conditions in banks’ local markets. Since banks make new business loan supply decisions simultaneously

with new real estate and consumer loan supply decisions, the right-hand side NLCt,i terms are endogenous,

and we account for this by estimating equation (4) using two-stage instrumental variables techniques. Full

details of our estimation methods appear below.

4.4. Predicted signs for estimated coefficients

Based on the discussion above, we can make the following predictions about the estimated

coefficients of equation (4):

• Same-sector loan overhang: Within the business loan sector, net lending change will be negatively

related to overhang (β1<0). This effect will be stronger when the sector is less liquid.

• Cross-sector loan overhang: If the portfolio model is the primary determinant of net lending changes,

then the impact of cross-sector loan overhang on net lending change (ρji) will be increasingly negative

(or less positive) as the covariance between loan losses in sectors i and j increases. Holding covariance

constant (and not equal to zero), the magnitude of ρji will be larger the more illiquid is loan stock j.

• Cross-sector net lending change: If our model holds strictly, the estimated effect of net lending change

in sector j on net business lending change (φji) should be the same sign as the estimated effect of sector

j loan stocks on net business lending change (ρji). The coefficients will be exactly the same (φji=ρji)

only if the loan stocks and net lending change have the same degree of liquidity and if loan losses for

each have the same correlation with loan losses for the net business lending change.

8 Estimating the model in its multiplicative form yields only trivial differences in the other coefficients.

17

• Risk tolerance: Within the business loan sector, net lending change will increase with the bank’s risk

tolerance (ξ>0).

• Risk-adjusted loan return: Within the business loan sector, net lending change will increase with the

risk-adjusted return ratio (χ>0). Effectively, this coefficient captures the risk-adjusted slope of the

business loan supply function.

5. Market imperfections and small bank lenders

The assumptions underlying our theory (i.e., imperfect capital markets, loan illiquidity, risk averse

lending decisions) are especially descriptive of the business lending environment faced by small

commercial banks. The limited lending capacity of these banks precludes them from making or

participating in business loans to large publicly traded firms; instead, small banks specialize in business

loans to small, privately-held businesses that are opaque to public capital markets. These loans typically

rely on relationships between a small bank’s loan officers and its business borrowers that allow the bank to

observe soft (i.e., not quantifiable) information about the borrower that can be used to evaluate the

borrower’s creditworthiness (Stein 2002). Although relationship loans are not based solely on soft

information—for example, banks usually require collateral for which a hard value can be determined—

these loans remain far less liquid than loans based solely upon quantifiable information.9 They are not

securitizable and can be sold to other banks only at large discounts, because the informational value of the

borrower-lender relationship cannot be credibly conveyed to outside investors. Moreover, when a bank

makes a relationship loan it knows that such an option does not exist—the exit barrier created by these

loans serves as an entry barrier for (larger, hard information-based) lenders that wish to avoid the illiquidity

9 While a large portion of these loans have short maturities, confusing maturity with liquidity belies the nature of the long-term borrower-lender relationship at the core of small banks’ business lending strategies. All else equal, community banks will be reticent to allow these loans to roll off their balance sheets, as this represents the loss of intangible relationship value in which the bank has invested. Moreover, as per Rajan (1992), the borrowers are likely to face informational lock-in costs if they try to repay their lender by seeking other sources of finance. Thus, the short (usually one-year) contractual maturities of small business credit lines are better interpreted as a risk-management tool that provides a periodic opportunity for adjusting loan terms and prices.

18

that comes with relationship lending. Berger et al. (2005) find evidence consistent with this description.

Similarly, the real estate loans and consumer loans made by small banks may be less liquid than

those made by larger banks. Large banks originate with the intent to securitize large portions of their real

estate loans (e.g., residential mortgages, home equity lines of credit) and consumer loans (e.g., auto loans,

student loans, credit card receivables). The originate-and-securitize production process generates additional

costs that are not present in portfolio lending (e.g., legal and credit rating agency fees, overhead for

performing statistical analysis, establishing a reputation in the asset-backed securities market, providing

credit enhancements to the buyers of the asset-backed securities), but these additional expenses may be

more than offset by reduced expenses for credit screening, increased noninterest revenues (from mortgage

origination, servicing and securitization fees) and cost scale economies associated with this production

process. Because high volumes of loan origination are necessary to run this process efficiently, and because

selling off rather than holding loans is antithetical to close bank-borrower relationships, small banks

typically choose to securitize only a small portion of the real estate and consumer loans they originate, and

hold a larger portion as portfolio investments. The principle exception to this are conforming home

mortgage loans sold to government-sponsored enterprises such as Fannie Mae, Freddie Mac and Ginnie

Mae.

Small banks are also more likely to be sensitive to the risk overhang effects associated with illiquid

loan portfolios. These lenders lack access to public funding markets; this increases their cost of external

financing, which in turn magnifies the consequences of all new lending decisions. Because credit

derivatives are not a viable hedging strategy for these banks (CDS do not exist for small business loans,

and using existing CDS to hedge these loans would entail extreme basis risk), they must manage risk in

their loan portfolios by adjusting on-balance sheet loan concentrations. And small bank managers are often

placing their family’s capital at risk when making lending decisions (community banks are often owner-

managed), so risk-averse lending behavior should be relatively free of potentially confounding principal-

agent effects (DeYoung, Spong and Sullivan 2001; Spong and Sullivan 2007).

All of these small bank sensitivities likely grew stronger during the financial crisis, when access to

19

liquidity in general became tighter. Data from the fed funds market—a major source of short-run liquidity

for small and large banks alike—is indicative. Small U.S. banks (defined here as banks with less than $2

billion in assets) tend to be deposit-rich, while large U.S. banks (defined here as banks with more than $50

billion in assets) tend to be deposit-poor, and in normal times the fed funds market transfers excess liquidity

from small banks to large banks. Prior to the crisis, fed funds sold fluctuated between 3% and 5% of small

bank assets, but fell to only about 2% of small bank assets during the crisis. Similarly, fed funds purchased

fluctuated between 10% and 12% of large bank asset funding prior to the crisis, but plunged to about 5%

during the crisis. These two developments are strongly linked: the quarterly time series correlation between

small bank fed funds sold-to-assets and large bank fed funds purchased-to-assets was 0.57 during the crisis

(2008-2010); this correlation was -0.03 during the 17 years leading up to the crisis. Hence, both large banks

and small banks experienced unusual liquidity pressure during the crisis: small banks felt it necessary to

hold higher stores of precautionary liquidity, and this resulted in a reduced supply of liquidity to large

banks.

6. Data and variables

We estimate the model using quarterly financial statement data for small U.S. commercial banks.

These data are taken from the Federal Reserve’s Report of Condition and Income (call reports) database

from the first quarter of 1991 (1991: Q4) through the fourth quarter of 2010 (2010:Q4). This sample period

includes data from before and during the global financial crisis. We define the beginning and the end of

the crisis based on the small business lending behavior by U.S. banks reported in the Federal Reserve’s

Senior Loan Officer Opinion Survey on Bank Lending Practices (SLOOS). The SLOOS is administered

four times each year to a relatively stable set of around 55 large and medium sized U.S. commercial banks.

Among other questions, the survey asks each bank whether its credit standards for approving small business

loan applications have eased, remained unchanged, or tightened over the past three months. Not

surprisingly, banks reported that they tightened lending standards early in the crisis, and reported that they

eased lending standards as the crisis waned. The net percentage of banks tightening their small business

20

lending standards exceeded 10 percent for the first time in the January 2008 SLOOS, so we mark 2007:Q4

as the beginning of the crisis. The net percentage of banks easing their small business lending standards

exceeded 10 percent for the first time in the April 2011 SLOOS, so we mark 2010:Q4 as the final quarter

of the crisis.10 Hence, we refer to the 64 quarters of data from 1991:Q4 though 2007:Q3 as the ‘pre-crisis’

period and the 13 quarters of data from 2007:Q4 through 2010:Q4 as the ‘crisis’ period.

We apply three primary filters to select the banks in our data set. First, for the reasons stated above,

we include only small, so-called community banks with less than $2 billion in assets in real 2010 dollars.11

Second, we only include banks located in urban geographic areas (in SMAs); banks located in rural areas

face a different set of lending opportunities than urban banks, which results in different exposures to loan

overhang and different incentives for dealing with this risk.12 Third, we only consider banks that make non-

trivial amounts of business loans, real estate loans, and consumer loans—the three main categories of loans

reported in the call reports. We define these ‘non-specialist’ lenders each period as follows: the dollar value

of their sector i loans must be no more than ten times, and no less than one-tenth, of the dollar value of

either of their sector j loans (i≠j).13 As shown in Figure 1, the asset share of real estate loans for the average

non-specialist bank approximately doubled during our sample period before declining somewhat during the

10 In the January 2008 SLOOS, 17 banks tightened standards, 39 did not change their standards, and 0 eased their standards. Thus, the net percentage of banks that tightened standards = (17–0)/56 = 30.4%, up from just 9.6% in the previous survey. In the April 2011 SLOOS, 0 banks tightened standards, 45 did not change their standards, and 7 eased their standards. Thus, the net percentage of banks that eased standards = (7–0)/52 = 13.5%, up from just 1.9% in the previous survey. 11 For decades, both bank regulators and bank researchers used $1 billion as a convenient upper size threshold to define the U.S. community bank sector (DeYoung, Hunter, and Udell 2004). Our $2 billion threshold is similarly convenient, but recognizes several decades of inflation. 12 Rural banks typically have local market power; with greater rents at stake, their ability and willingness to absorb risk overhang may differ markedly from those of urban banks. The extreme localness, or ‘ruralness,’ of these banks influences the manner in which they underwrite loans and results in lower levels of credit risk (DeYoung, Glennon, Nigro and Spong 2011). Rural banks hold relatively low levels of total loans, high levels of marketable securities, and high levels of equity compared to similarly sized urban banks (DeYoung, Hunter, and Udell, 2004), consistent with a less sophisticated approach to risk management. And because the agricultural economy permeates the performance of all lending sectors at rural banks (e.g., business loans are dominated by agricultural production loans and loans to farm-related business concerns, and real estate loans include large amounts of farm mortgages and farm residential mortgages), the loan performance covariances will differ from those observed in urban markets. 13 These upper and lower boundary restrictions eliminated around one-third of the bank-quarter observations and became more binding over time. To test whether these restrictions introduced selection effects, we re-estimated our basic models using a data set that included both specialist and non-specialist lenders (not shown, results available upon request). In nearly all cases, the estimated coefficients carry the same signs, statistical significance, and order of magnitude as those generated using the non-specialist bank-only data set.

21

financial crisis; the asset share of consumer loans declined by about half during our sample period; but the

asset share of business loans remained relatively stable over time.14 As real estate loan shares increased,

and consumer loan shares decreased, fewer banks qualified as non-specialist lenders; hence, the number of

observations in our tests unavoidably declines over time.

We make a number of additional adjustments to mitigate the potential effects of data errors,

merging banks, or banks with abrupt changes in lending strategies. We delete bank-quarter observations in

which the assets of another bank are acquired, bank-quarters when banks are less than 5 years old or less

than $25 million in assets, all observations for banks that lend out fewer than 25% of their assets, and all

observations for banks that were not present in the data for at least five consecutive quarters. We delete

bank-quarter observations when the ratio of nonperforming loans to beginning-of-period loans, the ratio of

net lending change to beginning-of-period assets, the quarterly change in assets, or the quarterly change in

equity capital are over the 99th percentile or below the 1st percentile of the sample distributions. Similarly,

we delete bank-quarter observations when the expected profit variable in any of the three loan sectors is

less than the 0.5th or greater than the 99.5th percentile of the sample distribution.

6.1. Regression variables

The empirical versions of the variables in theoretical loan supply equation (4) are defined in Table

1. Descriptive statistics for these structural variables, as well as all other variables used in our estimations,

are displayed in Table 2. We define the existing stock of loans Lt-1,i for three categories of loans: business

loans (BUS), real estate loans (RE) and consumer loans (CON) and the end of quarter t-1. Each of these

three broad categories contains different types of loans; this high level of aggregation is unavoidable given

the structure of the call reports.15 BUS includes all commercial and industrial loans. RE includes all loans

14 The sum of these three loan-to-asset shares increases over time. This mirrors the secular increase in total loan-to-asset ratios at small U.S. banks during the post-deregulation era, during which increased competition and industry consolidation removed inefficient banks that loaned out only a small portion of their assets (DeYoung, Hunter and Udell 2004, Tables A1 and A2). 15 While the call reports do disaggregate the portfolio balances for BUS, RE and CON loans into a variety of sub-categories, they do not similarly disaggregate the loan interest revenues associated with these sub-categories. This prevents us from calculating risk-adjusted loan returns (RAR) for loan sub-categories, and as such we are limited to using only the three highly aggregated loan categories in our tests.

22

secured by a lien on real estate: commercial and development loans, first and second mortgages on single

family and multi-family residential properties, and mortgages on commercial properties. CON includes all

revolving, installment, or single payment loans to individuals (e.g., auto loans, student loans, personal lines

of credit), with the exception of credit card loans which we exclude because they are relatively unimportant

for small banks.16 We normalize BUS, RE and CON by end-of-quarter t-1 bank assets to control for bank

size. We define new lending supply NLSt,i (or net lending change NLCt,i) for business loans (NEW_BUS),

real estate loans (NEW_RE) and consumer loans (NEW_CON) as follows: end-of-quarter t loan stock minus

end-of-quarter t-1 loan stock, plus net loan charge-offs (loans charged off minus loans recovered) during

quarter t. Again, we normalize by t-1 bank assets.17

The statistics displayed in Table 3, Panel B provide confirmation that business loans are on average

less liquid, and exhibit greater credit risk, than consumer and real estate loans. Credit risk data are

displayed in item 1. For the banks in our sample, business loans have the largest average quarterly loan

charge-off ratio (0.65%), followed by consumer loans (0.51%) and then real estate loans (0.10%). This

ranking is unchanged when specialist lenders are included in the averages. Although real estate loans

defaulted at high rates during the financial crisis, they have historically exhibited a relatively low level of

credit risk. Loan liquidity data are displayed in item 2. Unfortunately, the call reports do not contain

complete or uniform data on loan liquidity across loan types or across time. We use the sum of the best

variables available—“Outstanding principal balances of assets sold and securitized by the reporting banks

with serving retained or with recourse or other seller-provided credit enhancements” plus “Assets sold with

recourse of other seller-provided credit enhancements and not securitized by the reporting bank”—to

construct loan liquidity ratios for the second half of our sample. For the banks in our sample, business loans

16 Small banks exited credit card lending with the development of loan production processes (i.e., credit scoring and loan securitization) that exhibited huge scale economies. For the banks in our data, credit card loans never exceeded 1% of bank assets on average during our sample period. Loans to government entities, loans to other financial institutions, loans to finance agricultural production, and loans to finance the purchase of farm land also comprise a negligible portion of the loan portfolios of the small, urban banks in our sample. 17 In the theory model we assume that loans are perfectly illiquid and once made never leave the balance sheet. Hence, the theoretical term NL is non-negative. In contrast, our empirical proxies for NL are often negative because actual bank loans are only imperfectly illiquid, and can leave the balance sheet via sales, maturity, or charge-offs.

23

are the least liquid ( 0.07%), followed by consumer loans (1.01%) and then real estate loans (1.29%).18

Again, this ranking is unchanged when specialist lenders are included in the averages.19

Specifying (pt,1-µt,1)/σ11 for business loans is an imperfect exercise and involves making some

choices. In our main tests, we define risk-adjusted returns on business loans (RAR) as the ratio of the bank-

specific expected returns on business loans in quarter t divided by the market-specific variance of these

returns over the preceding twenty quarter period. The numerator in this ratio is the expected percent return

(the bank’s interest and fee income from business loans during period t, divided by its stock of accruing

business loans at the beginning of period t) multiplied by the expected performance of business loans (the

within-state percentage of performing loans averaged over the preceding twenty quarters) minus the average

deposit rate paid by the bank (the interest paid on deposits during period t divided by the average deposits

in the current and prior period). The denominator in this ratio is the quarterly variance of the within-state

quarterly average of the numerator over the preceding twenty quarters. By measuring loan performance

and expected return variance at the market level, we capture average risk in the pool of small businesses

from which the bank is drawing its loans; this specification reduces (though does not eliminate) problems

associated with endogenous business loan returns. While we believe that ‘expected’ loan returns is the

theoretically appropriate return concept, we also specify two other measures of RAR: ‘realized’ loan returns

and ‘perfect foresight’ loan returns. Appendix B contains detailed definitions of these alternative RAR

concepts and compares their performance in robustness tests of our baseline models. There is no evidence

that these alternative measures of RAR perform better than our preferred RAR definition.

We define bank-specific risk tolerance G-1 as the bank’s total equity capital divided by its total

18 The small magnitudes of the liquidity ratios understate the extent of loan liquidity for two reasons. First, small banks do not sell loans continuously throughout the year; hence, in any given quarter, the average ratios contain lots of zeros. Second, these data report only loans for which the selling bank is still exposed to recourse or other credit guarantees, which often expire with a year after the loan has been sold. 19 Not surprisingly, the specialist lenders exhibit higher overall levels of both credit risk and loan liquidity. By specializing rather than diversifying, these banks (a) are signaling that they are willing to operate with higher levels of credit risk and (b) must rely more on loan sales to manage their risk profiles.

24

assets at the beginning of quarter t (EQ).20 Intuitively, banks with lower financial leverage (higher equity

capital) will in general be more risk tolerant in their lending decisions: they are better able to absorb loan

losses and better able to sustain increased illiquidity in any one loan sector without making compensating

adjustments in other portions of their loan portfolio.

Note that, because the preferences of bank managers are idiosyncratic, the intrinsic level of

managerial risk aversion may vary across banks, with more risk-averse managers holding more capital on

average and less risk-averse managers holding less capital on average. Our fixed effects estimation

techniques will absorb these cross-section differences. Thus, the estimated coefficient on EQ will reflect

how an increase (decrease) in capital relative to that bank’s average capital will create (deplete) a capital

cushion and allow the bank to act in a more (less) risk tolerant fashion.

6.2. Loan performance covariances

In our theory model (3), the cross-sector overhang effects of non-business loans on new business

loan supply are explicitly related to the sign of the loan performance covariances (σij). In our empirical

model (4), however, the influence of these covariances on new business loan supply is absorbed into the

estimated coefficients ρji and φji. Hence, we need to observe the loan performance covariances in the data

in order to predict for the signs of these two coefficients.

Table 4 displays the number and percentage of banks in our data for which these covariances are

positive, where loan performance is measured as expected returns (pt - µt).21 For both pairs of loans, the

performance covariances tend to be negative: Cov(BUS,CON) is positive for 46.1% of the banks,

Cov(BUS,RE) is positive for 43.6% of the banks, and both figures are statistically different from 50%.

20 We construct EQ using the book values of equity and assets. The component parts of the Basel I risk-adjusted capital ratios are not available for our entire 1991-2010 sample period. 21 Although the theoretical loan supply function in (3) is expressed in terms of co-movements in nonperforming loans, in our empirical implementation we focus on co-movements in expected loan returns (e.g., for business loans, this would be the numerator from RAR). Banks have incentives to delay reporting reductions in loan quality, which requires them to make additional provisions for loan losses that reduce accounting net income. Given that we use quarterly data in our tests, even short delays in making these accounting adjustments will be problematic for our tests. Our measure of expected loan returns (pt - µt) does not rely on discretionary judgments by individual banks (e.g., the historical level of performing loans in this calculation is a state-wide average); hence, the covariances reported in Table 4 should be more accurate indicators of expected co-movements in loan performances.

25

Negative covariances suggest the existence of diversification gains from mixing business loans with real

estate loans and/or consumer loans in banks’ loan portfolios.22 More importantly, our theory model strictly

predicts positive signs for the cross-sector overhang and cross-sector net lending coefficients ρji and φji

when these covariances are negative. In empirical application, however, these predictions are weak ones.

First, the split between positive and negative covariances is close to 50-50, so our empirical expectations

of positive signs on RE, NEW_RE, CON and NEW_CON are not strong ones. Second, while the theory

model assumes that all loans are perfectly illiquid, home mortgage loans were far from illiquid investments

during our sample period; hence, we have less confidence in the prediction of positive coefficients for RE

and NEW_RE.

7. Estimation and identification

For clarity, we re-express equation (4) here using the variable names just described plus several

additional right-hand side terms:

tititititi

tiCONtiBUStiRE

tiCONtiREti

TBDSEQRAR

CONBUSRE

CONNEWRENEWBUSNEW

,,,,

1, 1, 1,

, , ,

__ _

εγϕωξχ

βββ

φφα

+⋅+⋅+⋅+⋅+⋅+

⋅+⋅+⋅+

⋅ +⋅ + =

−−− (5)

where i indexes banks, t indexes time in quarters, B indicates bank fixed effects, T indicates time (quarters)

22 Given that the locally focused banks in our sample are not diversified across regional business cycles, one might expect largely positive loan performance covariances. There are a number of reasons for negative covariances in loan performance. Historically, households under stress have tended to default on consumer loans (auto loans, credit cards) relatively early in a recession while continuing to service their home mortgage loans (Andersson, et al 2013). While small banks have local geographic focus in business lending, it is not unusual for them to make out-of-market real estate loans. The financial health of the average local household will be more closely related to local economic conditions, while the financial health of local businesses that export goods and services to other geographic markets will be exposed to non-local economic conditions. By construction, our measure of expected loan performance (pt - µt) increases with the ex ante risk spreads in the loan contracts; these risk spreads reflect local conditions for business loans, but follow economy-wide conditions for mortgage and consumer loans.

26

fixed effects, DS is a vector of business loan demand shifters, and the error term ε is normally distributed

around zero. We refer to equation (5) as our baseline regression model. In all of the estimations results

reported below, standard errors are clustered at the bank level.

Three methodological adjustments allow us to more cleanly identify the coefficients in equation

(5). First, we embed information on SME loan demand into the vector of demand shifters DS, based on

changes in business loan demand conditions reported to the Federal Reserve by commercial bank loan

officers during our sample period. Second, we instrument for the two obviously endogenous right-hand

side variables in our model (NEW_CON and NEW_RE) as well as for the potentially endogenous right-hand

side variable RAR. Third, we use both exogenous shocks during our sample period, as well as exogenous

variation within our data sample, to increase our confidence that the statistical associations that we find in

the data are actually strong tests of our theory. We explain these three methodological adjustments in order.

7.1. Business loan demand

The Federal Reserve reports changes in the demand for loans by small and medium sized

businesses, based on its quarterly Senior Loan Officer Opinion Survey (SLOOS). These data, which begin

in 1991, reflect the responses to a battery of in-person questions asked of senior loan officers at both large

and mid-sized U.S. commercial banks in each of the twelve Federal Reserve Districts. We draw our data

from the responses to question 4b: “Apart from normal seasonal variation, how has demand for C&I loans

changed over the past three months, from small firms with annual sales of less than $50 million?” The

surveyed loan officers have five choices—substantially stronger, moderately stronger, about the same,

moderately weaker or substantially weaker—and the Federal Reserve makes public the net percentage of

loan officers reporting stronger loan demand each quarter.

While the SLOOS data provide us with a high quality time series measure of the average fluctuation

in SME loan demand each quarter, these data contain no cross sectional variation.23 We gain cross-sectional

23 The SLOOS is a confidential survey. We requested, but were denied, access to the disaggregated (region-by-region) data for Question 4b. Nevertheless, these region-by-region averages would have provided us with only a limited amount of cross sectional variation. (For example, the quarterly averages for the 12th Federal Reserve District combine data from nine very different and far-flung western states.)

27

variation in small business loan demand by combining these quarterly SLOOS data with state-specific

economic conditions that should be related to business loan demand—for example, the quarterly state

unemployment rate, Unemployment Rate. For each of the fifty states in our data, we estimate a separate

time series regression of the state unemployment rate on the SLOOS measure of business loan demand

conditions. The quarterly fitted values of these regressions should contain only information on fluctuations

in local economic conditions that are related to SME loan demand. We repeat this process for two additional

measures of state-level economic conditions (the quarterly percent change in unemployment,

%∆Unemployment, and the quarterly percent growth in personal income, Per Capita Income) and use the

resulting set of three fitted values as our vector of demand shifters DS.24

In Table 6 below, we estimate two baseline versions of equation (5): once using the raw values of

Unemployment Rate, %∆Unemployment and Per Capita Income, and then again using the fitted values of

these demand shifters as described here. The fitted versions have larger coefficients, are more statistically

precise (both individually and as a group), and have economically intuitive signs.

7.2. Endogenous right-hand side variables

Because banks make their lending decisions in each loan sector i simultaneously, NEW_RE and

NEW_CON are endogenous by definition in equation (5). If community banks have market power in small

business lending (Petersen and Rajan 1995), then the right-hand side variable RAR in equation (5) is also

potentially endogenous. We use standard two-stage least squares instrumental variables (2SLS-IV)

estimation methods to address this endogeneity.

We select four instruments, all of which we observe at the state-level and vary across time:

24 Each of the state-level economic conditions variables are seasonally adjusted. Data on personal income growth are from the Bureau of Economic Analysis; data on unemployment rates and unemployment growth are from the Bureau of Labor Statistics. These measures should be strongly related to local businesses’ demand for credit: all microeconomics textbooks list household income—and hence employment—as key theoretical driver of household demand for goods and services, which in turn should be strongly correlated with sales by small businesses and hence their own demand for credit. While these measures also contain information correlated with small business loan supply, this information should be left in the time series residuals and hence will not enter the demand shifters. Because the banks in our sample are all very small relative to state-level macro-economic conditions, these measures are clearly exogenous to the banks’ business lending decisions.

28

unexpected (actual minus historical median) snowfall, the percentage of vacant rental units, the average

marginal tax rate (federal plus state) on personal income, and traffic fatalities per licensed drivers. First,

these instruments are clearly exogenous to the banks in our data. Second, these instruments can be excluded

from the second-stage regression. For instance, NEW_BUS should be largely unaffected by weather

conditions because the call report definition on which it is based (C&I loans) excludes loans for weather-

sensitive construction or agriculture projects, should be unrelated to rental vacancies because its call report

definition explicitly excludes loans that are secured by real estate, and should be relatively unrelated to

personal tax rates because the large majority of banks in our sample are taxed at the corporate level.25 Third,

there are plausible reasons to expect these instruments will be correlated with the right-hand side

endogenous variables. Extreme winter weather conditions can affect construction schedules and hence are

related to the supply of real estate loans; weather can also alter consumer purchase behavior and hence the

supply of consumer loans.26 Changes in rental vacancies should be related to the number and size of

residential housing loans, while personal tax rates should be related to the number and size of consumer

loans. Traffic fatality data capture variation in a number of primary factors—such as highway conditions

(and hence investment in infrastructure), commuting distances (and hence the real estate rent gradient and

automobile longevity) and destroyed vehicles—that may be correlated with variation in loan supply. 27 By

similar reasoning, these four instruments should also be correlated with bank profitability and risk (RAR).

As displayed in Appendix A, each of these four instrumental variables is statistically significant in

at least one of the first-stage regressions and the coefficients tend to have economically sensible signs.

Moreover, when we included these instruments in the second-stage regressions, they had statistically non-

25 Only 13.7% of the bank observations in our sample were organized as Subchapter S corporations, in which all bank earnings are passed through to shareholders and fully subject to personal income tax. 26 Construction company contracts include clauses that extend deadlines if rainfall or snow totals exceed amounts that will make it difficult to deliver their projects on time, especially in winter season. 27 Traffic fatalities are projected to be the fifth leading cause of death by 2030 (World Health Organization 2009). The economic damage done by traffic accidents and fatalities—e.g., the destruction of vehicles, the loss of goods being shipped by trucks, the death of employees—has been estimated equivalent to one percent of national output in the typical country (Fouracre and Jacobs 1976). Replacing these lost resources is likely to have nontrivial effects on financial institution profitability, via additional loans and insurance policies.

29

significant coefficients (results not shown, available upon request).

7.3. Exploiting exogenous variation

In our baseline estimates of equation (5) in Table 6, we rely solely on variation in the right-hand

side variables BUS, CON, RE, EQ, and RAR to identify our risk overhang tests. For four of these five

variables, the baseline tests generate statistically and economically significant coefficient estimates with

signs consistent with the predications of our theory.28 In a series of additional tests displayed in Tables 7

through 11, we exploit exogenous variation in state tax laws, bank tax status, macro-economic conditions

and long-term bank lending strategies to more strongly identify our risk overhang tests. These additional

tests tend to generate even stronger economic and statistical evidence consistent with our theory.

7.3.1. The crisis and bank lending strategies. The main objectives of this study are (a) to determine

whether the financial crisis caused a significant reduction in small banks’ loan supply to SMEs, and if so,

(b) to test whether and how the reduction in SME loan supply varied across bank lenders. Recent studies

of bank loan supply in Europe (e.g., Popov and Udell 2010, Puri, Rocholl and Steffen 2011, Jimenéz et al

2012) have gained the identification necessary to address objective (a) by exploiting exogenous

heterogeneity (natural experiments), detailed loan-level credit registry databases, and/or firm-level survey

data. Unfortunately for us, firm-level and loan-level data for SMEs and SME lenders in the U.S. is

extremely limited; moreover, there is no obvious useful natural experiment (other than the financial crisis

itself). Given these data limitations, we must address objective (a) using much coarser bank-level (as

opposed to loan-level or firm-level) data—but this is the natural empirical approach for testing the bank-

level predictions of our theory model in pursuit of our objective (b).

We define a financial crisis dummy variable CRS that is equal to one for all quarterly observations

from 2007:Q4 through 2010:Q4, and we interact CRS with each of the main test variables BUS, RE, CON,

EQ and RAR in equation (5). The CRS dummy is doubly useful: not only was the financial crisis an

28 The coefficient on RE is statistically zero in our baseline tests, and continues to be zero in all but a few of our subsequent tests. As discussed below, this is likely due to data limitations that force us to combine very different types of real estate-backed loans (e.g., home mortgages with construction and development loans) into the single RE variable.

30

exogenous shock, it was associated with loan write-downs that reduced internal bank equity capital, an

increased cost of raising external equity finance (stock price declines) and reduced opportunities to sell

loans in secondary markets and/or into loan securitizations—conditions under which our hypothesized risk

overhang effects should be stronger. For example, to test whether the financial crisis was associated with

a reduction in small business loan supply and whether our hypothesized risk tolerance effect played a role

in any such reduction, we specify the right-hand side of (5) to include the following terms:

,2,1 ttitit CRSEQEQCRS ⋅⋅+⋅+⋅ ξξλ (6)

where the impact of the crisis on the supply of new business lending is given by ,2 tiEQ⋅+ ξλ and a

positive value for 2ξ would indicate that bank risk tolerance mitigates crisis-driven reductions in lending.

Still, the approach shown in (6) provides only weak identification of the hypothesis in question,

because the estimates of λ and 2ξ will capture all of the changes in the bank lending environment

contemporaneous with the crisis, not just those associated with the hypothesis (i.e., risk tolerance) we are

testing. We strengthen our tests by adding a third interaction term that identifies banks with ex ante illiquid

loan portfolios—according to our theory, the small business lending behavior of these banks should exhibit

especially strong risk overhang effects during the crisis. We note that SME loans and commercial real

estate loans are more illiquid than other types of loans held in bank loan portfolios—the illiquidity of SME

loans is a well-established fact, and the illiquidity of commercial real estate loans is supported by recent

research by Levitin and Wachter (2012), who report that approximately 80% percent of U.S. commercial

real estate debt in 2011 was held in portfolio rather than securitized, and even higher percentages were held

in portfolio during the 1990s and early 2000s.29 We define an arguably exogenous ‘commercial focus’

dummy COMM that equals one at time t if the bank was in the highest quartile of commercial loans (in our

29 In contrast, the majority of retail loans—e.g., auto loans, student loans, home mortgage loans—are securitizable, as they are underwritten based on credit scores, are highly collateralized, and/or carry government or private guarantees.

31

data, BUS plus the portion of RE comprised of commercial real estate loans), and also in the lowest quartile

of retail loans (in our data, CON plus the portion of RE not comprised of commercial real estate loans), in

each of the past 10 quarters (t-11 through t-1). We choose this 10-quarter time threshold based on the

results of the Kaplan-Meier hazard estimation in Figure 2, in which the probability of a bank switching

away from this commercial focus strategy falls below 1% after having engaged in this strategy for 10

consecutive quarters. Thus, COMM captures exogenous cross sectional variation in banks’ business models

and also reflects differences in the illiquidity of banks’ existing loan stocks. About 13% of the observations

in our sample have ‘commercial focus.’ For ease of exposition, we will refer to the remaining 87% of the

observations in our sample as having ‘retail focus.’ Table 5 compares the average composition of the loan

portfolios at these two sets of banks.

We can now specify a stronger set of tests by expanding (6) to include the following set of terms:

tittititi

ttititit

COMMCRSEQCOMMEQ

CRSEQEQCOMMCRS

,,4,,3

,2,1,

⋅⋅⋅+⋅⋅+

⋅⋅+⋅+⋅+⋅

ξξ

ξξηλ (7)

This specification employs a difference-in-difference logic in which CRS is the treatment variable and

COMM is the control variable. The impact of the crisis on the supply of new business lending is now given

by ,4,2 COMMEQEQ titi ⋅⋅+⋅+ ξξλ where a positive value for 4ξ would indicate that the bank risk

tolerance effect is strongest when banks conform most closely to the maintained assumptions of our theory

model, i.e., that banks hold illiquid loans. Applying this identification scheme to each of the main test

variables—not just to EQ, but also to BUS, RE, CON and RAR—provides strong and internally consistent

identification for each of the main predictions of our theory.

7.3.2. Tax status and tax rate shocks. We construct a second alternative specification that exploits

exogenous variation in the tax status of our sample of banks and exogenous shocks to the tax rates applied

32

to the profits of those banks during our sample period. First, let SUB_S be a dummy variable equal to one

when bank i is organized as a subchapter S corporation at time t. The profits of subchapter S firms are not

exposed to double taxation: net income passes through to shareholders untaxed and is exposed only to

personal income taxes. In exchange for this favorable tax treatment, subchapter S firms cannot be widely

held and must maintain a high dividend payout. Because these restrictions reduce their ability to raise both

internal and external equity capital, risk overhang effects should be especially strong at subchapter S banks.

It seems reasonable that the decision to organize as an S corporation is a fixed decision and is not

systematically related to the bank’s supply of new business loans, which is just one of the several financial

products produced by the non-specialist banks in our sample. Second, let TAXINC be a dummy variable

equal to one during each of the first four quarters after state personal tax rates increased in bank i’s home

state. We derive this variable using data from the National Bureau of Economic Research (NBER) Taxsim

model of U.S. taxpayers. A personal income tax increase will further raise the cost of internal equity capital,

because shareholders will require a higher dividend payout to cover their increased tax liabilities. For the

risk tolerance effect, the new right-hand side specification will include the following terms:

tittititi

ttititit

SSUBTAXINCEQSSUBEQ

TAXINCEQEQSSUBTAXINC

,,4,,3

,2,1,

_ _

_

⋅⋅⋅+⋅⋅+

⋅⋅+⋅+⋅+⋅

ξξ

ξξηλ (8)

This specification also employs a difference-in-difference logic in which TAXINC is the treatment variable

and SUB_S is the control variable. The impact of the tax increase on the supply of new business lending is

now given by _ ,4,2 SSUBEQEQ titi ⋅⋅+⋅+ ξξλ where a positive value for 4ξ would indicate that the

bank risk tolerance effect is strongest when banks conform most closely with the maintained assumptions

of our theory model, i.e., that external capital is costly. We apply this identification scheme to each of the

main test variables—not just to EQ, but also to BUS, RE, CON and RAR. We also include an additional

33

stand-alone variable TAX CHANGE on the right-hand side, a continuous measure of the change in the state

marginal personal tax rates from the Taxsim model.30

While specification (8) provides another clean test of the risk overhang predications of the theory

model, it does not provide a test of our main question of interest, i.e., whether the financial crisis resulted

in reduced business loan supply by U.S. community banks. Moreover, because U.S. commercial banks

were prohibited from organizing as subchapter S corporations prior to 1997, we cannot estimate this

specification for our full sample period.

7. Results

We begin by estimating equation (5) as written above. These baseline estimates are substantially

in-line with the predications of our theory model. Moreover, these estimates provide strong indications that

our controls for business loan demand, as well as our treatments for endogeneity (new consumer loan

supply, new real estate loan supply, risk-adjusted returns), are performing effectively. To generate cleaner

tests of the theory, we augment the model specification as described in equations (7) and (8) and estimate

it using exogenous variation in the market imperfection highlighted in the theory (loan illiquidity, equity

capital supply, bank risk aversion). Importantly, the data indicate that new business loan supply from small

commercial banks declined during the financial crisis on average, with the exception of banks with a

commercial lending focus which increased their supply of new business loans during the first year of the

crisis. In addition, the evidence is consistent with stronger business loan overhang effects, stronger risk

tolerance effects, and business loan credit rationing, during the financial crisis.

7.1. Baseline model

The results from our baseline model (5) are displayed in Table 6. We use both panel OLS and

2SLS-IV estimation techniques and we employ two different versions of the business loan demand shifters

30 We include the continuous variable TAX CHANGE to soak up any variation in loan demand resulting from changes in the personal income tax rates, while allowing the separate dummy variable TAXINC to capture only the negative shock to subchapter S owners.

34

DS. Column 3 is our preferred specification, in which we use fitted demand shifters and instrument for all

three potentially endogenous regressors.

As expected, the same-sector overhang effect (BUS) is negative, statistically significant and

economically large throughout. Using the column 3 estimates, a 10% increase in overhanging business

loans is associated with a next quarter decline in new business lending equal to about 2.5% of a bank’s

outstanding business loan balances (BUS).31 This substantial one-quarter effect understates the eventual

impact of loan overhang, as the initial ‘shock’ will result in additional (though diminishing) quarterly

reductions in the quarters that follow. If we make the relatively reasonable assumptions that business loans

are illiquid, are originated uniformly across quarters, and have one-year maturities, then the cumulative

reduction caused by a 10% increase in overhanging business loans equals roughly 6.3% of outstanding

business loan balances.32

The cross-sector overhang effect for consumer loans (CON) is positive. Given that the Table 4

covariances between business and consumer loan returns tend to be negative, this result is consistent with

the predictions of our theory model. Based on the column 3 estimates, a 10% quarterly increase in

overhanging consumer loans is associated with an increase in net new business lending of about 1.5% over

the next four quarters. The cross-sector net lending change effect (NEW_CON) is also positive as

predicted—an additional dollar of new consumer lending is associated with a $0.23 increase in new

business lending—but this finding is not statistically significant.

The coefficients on RE and NEW_RE are both statistically zero in our preferred column 3

specification. Given that the Table 4 covariances between business and real estate loan returns tend to be

negative, our model strictly predicts positive signs for these coefficients. This strict prediction is based on

the assumption of perfect loan illiquidity, but we also show that these overhang effects will attenuate to

zero as loans become more liquid: setting δt-1,,j = 0 in equation 3′ above defuses the cross-sector overhang

31 The result is obtained by multiplying -0.0300 (the same-sector loan overhang coefficient in column 3) by 0.10 and then dividing the result by 0.1183 (the sample mean BUS). 32 The result is calculated as follows: -0.0300*(.10 + .075 + .05 + .025)/0.1183 = 0.0640.

35

effects regardless of the value of σij. Indeed, highly liquid residential real estate loans (home mortgages

plus home equity loans) comprise 53% of RE during our sample period. Levitin and Wachter (2012) report

that 62% of residential mortgages originated in the U.S. in 2011 were securitized, and that securitization

rates for these loans had been more than 80% prior to the financial crisis. The non-significant coefficients

on RE and NEW_RE are consistent with an option to sell that defuses the RE overhang effects.

As expected, the risk-adjusted return variable RAR carries a positive and statistically significant

coefficient throughout. Though we are not estimating a formal loan supply function, this result is strongly

consistent with a loan supply relationship: when the expected returns from making business loans increase,

banks supply more net business loans. Using the estimates in column 3, a one standard deviation increase

in RAR is associated with a next quarter increase in net new business lending equal to about 3.2% of a

bank’s outstanding business loan balances.33 Note that treating expected business loan returns as potentially

endogenous, and thus including RAR among the instrumented-for variables in column 3, substantially

increases the magnitude of the RAR coefficient and in a theoretically consistent direction. (In Appendix B

we re-estimate these baseline models using two alternative definitions of RAR: one that measures ‘realized

RAR’ and one that measures ‘perfect foresight RAR.’ Neither alternative measure outperforms the ‘expected

RAR’ measure used in Table 6.)

The risk tolerance variable EQ also carries a positive and statistically significant coefficient. Thus,

increases in banks’ capital cushions—the most basic form of credit risk mitigation at community banks—

are linked with increases in business loan supply. In column 3, a one standard deviation increase in EQ is

associated with a next quarter increase in net new business lending equal to about 0.22% of a bank’s

outstanding business loan balances. While this seems a small economic effect, one must remember that

book value equity (so-called ‘leverage capital’) supports the entire bank loan portfolio, not just business

loans. Given that business loans comprise on average only about 20% of total bank loans, the full impact

of increased risk tolerance on bank loan supply will be at least several times larger than this.

33 Multiplying the RAR coefficient (0.00221) by the standard deviation of RAR (1.59) and dividing by mean BUS (0.1183) yields the result.

36

We estimated the baseline model for two different versions of the demand shifters Per Capita

Income, %∆Unemployment and Unemployment Rate. In the first three columns of Table 6, these demand

shifters (DS) are fitted to the Federal Reserve SLOOS data on small business loan demand, as described

above. The coefficients on these fitted DS always carry the expected sign, are always statistically

significant, and are statistically significant as a group (F-statistics). In the final three columns of Table 6,

we simply use the raw values of the DS variables. The results imply that the theoretically superior fitted

DS are also empirically superior. The fitted DS carry substantially larger, more often statistically

significant, and collectively stronger coefficients than do the raw DS.

The diagnostic tests at the bottom of Table 6 indicate that our instruments for NEW_RE, NEW_CON

and RAR are relevant and valid. The p-values for the underidentification tests (where we seek to reject the

null) and overidentification tests (where we seek to not reject the null) are strong. The test statistics for the

weak identification test are border-line, about equal to the critical value above which the instruments are

strong at the 10% level; we note that this test statistic tends to clear the critical value by more comfortable

margins in the additional regression results reported below that use our full sample (see Tables 8, 10 and

11).

7.2. Identification using tax status and tax rate shocks

We attempt to more cleanly identify our tests by exploiting exogenous variation in bank tax status

within our data as well as exogenous shocks to the tax rates paid by those banks. We augment the baseline

model (5) to include a full set of the right-hand side terms introduced above in (8). SUB_S is a dummy

variable equal to one for banks organized as subchapter S corporations, while TAXINC is a dummy variable

equal to one during each of the first four quarters following an increase in state personal tax rates in the

bank’s home state. As explained above, subchapter S status effectively constrains a firm’s access to external

capital. Because banks were not permitted to use subchapter S of the U.S. tax code prior to 1997, we

estimate this version of our model for a much smaller number of bank-quarter observations.

The results are displayed in Table 7 and largely conform to our theory, which predicts that loan

overhang effects will be larger, and risk tolerance effects will be smaller, as external capital grows more

37

costly (or equivalently, less available). The same-sector overhang effect is substantially stronger for

subchapter S banks on average (coefficient on BUS*SUB_S = -0.0289) and is twice again stronger when S

corporation owners are faced with an increase in taxes (coefficient on BUS*SUB_S*TAXINC = -0.0624).

Comparing the partial derivatives in columns 2 and 5 shows the full effect of increasingly costly equity

capital on the same-sector business loan overhang effect—more than a three-fold increase.

We also find statistically significant increases in the cross-sector loan overhang effects for both

overhanging consumer loans (coefficient on CON*SUB_S*TAXINC = 0.0573) and overhanging real estate

loans (coefficient on RE*SUB_S*TAXINC = 0.0220). Moreover, the risk tolerance effect disappears

entirely for subchapter S banks (∂NEW_BUS/∂EQ is statistically zero in columns 3 and 5), a very reasonable

finding given that equity capital build-ups at these banks are largely targeted for distribution and hence are

temporary. The risk-adjusted return effect (partial derivative with respect to RAR) is statistically positive

for the C corporation banks (column 2) but is never statistically positive for the S corporation banks; this is

consistent with the spirit of our theory that new business loan supply is essentially return-inelastic at banks

that are funding constrained.

7.3. Impact of the financial crisis

We now address our main questions: Did the financial crisis cause a reduction in small business

loan supply from U.S. community banks? Do the data more strongly conform to the predictions of our

model (loan overhang, risk tolerance) when market imperfections grew larger during the financial crisis

(increased loan illiquidity, more costly external capital)? We augment the baseline model (5) to include a

full set of the right-hand side terms introduced above in (7). COMM is a dummy variable equal to one for

banks with long-standing strategies of lending to commercial borrowers, which all else equal reduces the

liquidity of their loan portfolios. CRS is a dummy variable equal to one during the financial crisis, during

which equity capital became more expensive.

The results are displayed in Table 8. On average, the results indicate that community banks did

reduce their supply of small business loans during the crisis. Our main test comes from evaluating the

derivative ∂BUS_NEW/∂CRS separately for the retail focused banks which comprise 87% of our sample

38

(COMM=0) and the commercial focused banks which comprise 13% of our sample (COMM=1). These

derivatives appear at the bottom of the table. At retail focused banks, net new business lending per dollar

of assets declined on average by 33 basis points per quarter during the crisis, an amount equal to 1.69% of

existing business loans at these banks.34 In contrast, new business lending per dollar of assets increased on

average by 157 basis points per quarter during the crisis for the commercial focused banks, or by about

4.79% of existing business loans at these banks. This result is stark: the typical (retail focused) community

bank effectively reduced its ongoing new supply of credit to SMEs by 6.5% (1.69% + 4.79%) during the

crisis relative to banks that were strategically dedicated to making and holding illiquid SME loans

(commercial focused banks).

It is well-known that the volume of commercial loans outstanding at U.S. banks continued to

increase well into the financial crisis—banks were not necessarily originating new loans, but rather firms

were for a time able to draw down their existing credit lines (Berrospide, Meisenzahl and Sullivan 2012).

The National Bureau of Economic Research (NBER) dates the U.S. recession as lasting from December

2007 to June 2009, but total commercial and industrial (C&I) loan balances at U.S. commercial banks did

not peak until 2008:Q3, and small business loan balances (defined as C&I loans with principle amounts

less than $1 million) did not peak until 2008:Q4. Both of these peaks were followed by sharp and long-

lasting declines in outstanding loans.35 In Table 9 we illustrate how the behavior of the banks we define

here as commercially focused partially mitigated the decline in SME lending during the recession. The

results come from models identical to the one in Table 8, with one exception: we replaced the CRS dummy

with a dummy equal to one in the first year of the recession (2007:Q4-2008:Q4), or in the second year of

the recession (2009), or in the third year of the recession (2010). Net new business lending at retail focused

34 The former result is simply the derivative with respect to CRS evaluated for retail focused banks. The latter result is produced by dividing the estimated derivative by the average BUS/LOANS ratio of 0.195 for the banks in this subsample. 35 Total C&I loans at U.S. banks peaked at $1.503 trillion in 2008:3Q, bottomed out at about $1.165 trillion in 2010:Q2-Q3, and then began a steady quarterly increase. Small business loans peaked at $0.336 at the end of 2008, but did not hit bottom until 2011, and since then have fluctuated between $0.278 and $0.285 trillion with no clear increasing trend (as of the date of this draft). The figures are based on data from the various editions of the FDIC Quarterly Banking Profile, http://www2.fdic.gov/qbp/index.asp.

39

banks declined during all three years of the recession, but increased at commercial focused banks during

the first year of the recession—which likely captures the aforementioned drawing down of pre-exiting lines

of credit—and then held steady without declining during the second and third years of the recession.

These findings imply the existence of valuable bank-borrower relationships at the commercial

focused banks in our data. Notably, these banks increased SME loan supply during the recession even

though they arguably suffered from greater loan illiquidity. For these banks, it appears that the value of

preserving bank-borrower relationships offset any crisis-induced reduction in asset liquidity (loan overhang

effects) or crisis-induced scarcity in equity capital (risk tolerance effects). Overall, these actions were not

enough to prevent the decline in total SME lending total during the financial crises, driven by retail focus

or mixed focus lenders for whom close relationships with business clients were relatively less important.

Returning to Table 8, we consider the channels through which small banks increased or decreased

business loan supply, both before and during the financial crisis. For pre-crisis banks (CRS=0) with retail

banking strategies (COMM=0)—that is, banks with relatively low amounts of loan illiquidity during times

of relatively plentiful and inexpensive equity capital—we obtain the following results: negative same-

sector overhang effects for business loans; positive cross-sector overhang and new lending effects for

consumer loans; zero cross-sector effects for real estate loans; positive risk tolerance effects; and positive

risk-adjusted return effects. The signs, significance and relative economic magnitudes of these results (see

column 2) are the same our baseline results in Table 6.

The loan overhang effects tend to be stronger both during the crisis (CRS=1) and/or for banks with

commercial lending strategies (COMM=1). The same-sector overhang effect (BUS) is larger for

commercial focus banks (coefficient on BUS*COMM) and during the financial crisis (coefficient on

BUS*CRS). Consistent with our theory, this effect increases to twice its baseline magnitude for the most

illiquid banks during the most illiquid quarters in our data (compare columns 2 and 5). Similarly, the cross-

sector overhang effect for consumer lending (CON) is larger for commercial focused banks both before and

during the crisis. The cross-sector overhang effect for real estate lending (RE) remains near zero in all four

40

cases.36

Also consistent with our theory, the risk tolerance effect (EQ) is larger for banks with more illiquid

loan portfolios (coefficient on EQ*COMM) and grows substantially larger for these banks during the crisis

(coefficient on EQ*CRS*COMM). Finally, the estimated risk-adjusted return effects (RAR) are consistent

with SME credit rationing during the financial crisis. For pre-crisis banks (columns 2 and 4) we find the

expected positive relationship between net new business lending NEW_BUS and expected business loan

returns RAR. But this positive loan supply effect disappears during the crisis (columns 3 and 5); the

unresponsiveness of SME loan supply to expected SME loan returns suggests that the decline in SME loan

supply during the crisis was the result of quantity rationing rather than price rationing.

7.4. Cross-study comparisons

It is instructive to compare the economic magnitudes of our results to those found in other studies.

Because we employ a substantially different empirical approach from other studies of SME loan supply

during the financial crisis, direct comparisons are difficult and for some studies impossible. Still, placing

some of these estimates side-to-side provides insight. We restrict our comparisons to studies cited above

that, like our study, estimate loan supply regressions that contain a right-hand side financial crisis variable.

In our bank-level study of small commercial banks in the U.S., we find that net new SME loan

volume declined by about 6.5% at the typical bank in our sample during the crisis (relative to the small set

of banks with long-established commercial lending strategies from which we gain identification). Jimenéz

et al (2012) estimate a model of SME loan application acceptance rates in Spain during the crisis. Using

their regression estimates, it is straightforward to calculate that the loan application acceptance rate

attributable to supply-side conditions declined by 554 basis points during the crisis, or about a 14%

reduction in the average acceptance rate.37 Puri, Rocholl and Steffen (2011) estimate a model of consumer

36 The outlying result here is the coefficient on RE*COMM, which is relatively small but statistically negative. This likely arises because real estate lending increases at COMM=1 banks will be heavily weighted toward commercial real estate loans, which are relatively illiquid loans that perform similar to BUS loans across the business cycle. 37 We performed these calculations using the linear probability estimates from the first column of Table 3, and the descriptive statistics from Table 1, in Jimenéz et al (2012).

41

loan application acceptance rates at Germany savings and loans during the crisis. At savings and loans that

were exogenously exposed to the financial crisis, mortgage loan application acceptance rates declined by

about 1150 basis points during the crisis, compared to an increased in acceptance rates of about 70 basis

points at savings and loans that were not exposed to the crisis. The relative difference represents about a

12.5% reduction in the average acceptance rate.38

It is not surprising that our estimates of loan reductions are smaller than those in the extant

literature—by necessary empirical design, our estimates understate the impact of the crisis on SME new

lending agreements. NEW_BUS includes net lending flows from both newly approved loan contracts and

from previously approved lines of credit; the latter phenomenon is partially offsetting the former in our

regressions, resulting in smaller estimated crisis-induced reduction in SME lending. Re-estimating our

models based purely on lending flows from newly approved loan contracts (i.e., netting out the drawdowns

of pre-existing loan contracts) would result in a larger lending reduction and more direct comparison to the

above studies, which are based solely on new loan applications. Unfortunately, the U.S. bank data do not

report separately drawdowns from existing facilities.

7.5. Robustness tests

Thus far, we have established that small banks in the U.S. reduced their supply of business credit

during the financial crisis, and we have provided strong suggestive evidence that three phenomena—

overhanging illiquid loans, reduced tolerance for risk, and credit rationing—were important drivers or

facilitators of this reduction in credit. We finish our analysis with a series of robustness tests to determine

the pervasiveness of our findings across the U.S. community banking sector.

First, we tested whether and to what extent our results are driven by banks that eventually failed,

and hence may not represent the long-run behavior of banks across the business cycle. To investigate, we

dropped all observations of banks seized and resolved out of existence (via forced mergers, asset

liquidation, or depositor payouts) by the FDIC during our 20-year sample period. We then re-estimated

38 The reduction in the average consumer loan application acceptance rate was smaller, about 7.5%.

42

our Table 8 model for the remaining subsample of financially healthy banks. These subsample results were

qualitatively identical and quantitatively very similar to the full sample results. (Results not shown,

available upon request.) We conclude that bank distress had little if any impact on our main findings.

Second, we tested whether our findings vary by bank size. It is common in empirical banking

studies to separate banks by asset size. While all of the banks in our data are relatively small to begin with,

they vary in size by two orders of magnitude, ranging from $18 million to $1.9 billion in assets. The

potential for loan portfolio diversification, access to short-run liquidity, the ability to hire skilled financial

professionals are all likely to increase non-trivially with bank size in this data set; hence, loan overhang and

risk tolerance effects may also vary across these banks. To investigate, we re-estimate our Table 8 model

after replacing the COMM dummy variable with a LARGE dummy variable, which equals one for banks

above the median value of bank assets during each quarter. The coefficient on the LARGE variable, the

coefficients on all ten of the variables with which LARGE was interacted, and the derivative

∂BUS_NEW/∂LARGE were all statistically zero in this specification. (Results not shown, available upon

request.) So at least within our sample of community banks (all with assets less than $2 billion), bank size

influenced neither the impact of the financial crisis on net new SME lending nor the strength of loan

overhang or risk tolerance effects on net new SME lending.

Third, we tested whether banks’ geographic diversification influenced their risk tolerance, their

sensitivity to loan overhang, or their response to the crisis. During the Great Depression—the deep

economic downturn to which the financial crisis is often compared—banks in states that freely allowed

branching were less likely to fail than banks in unit banking states that prohibited branching (Wheelock

1995), which suggests that broader geographic footprints yield diversification benefits that mitigate banks’

exposure to idiosyncratic credit risk. To test this thesis, we replaced the COMM dummy with the dummy

variable GEO, which equals one for banks whose deposits are well-diversified across counties.39 As with

39 We calculate a Herfindahl index of deposit concentration for each bank, based on the county-by-county dispersion of its deposits. A bank in the bottom quartile of the quarterly distribution of this index is considered to be well-diversified.

43

bank size, the coefficient on the GEO variable, the coefficients on all ten of the variables with which GEO

was interacted, and the derivative ∂BUS_NEW/∂GEO were all statistically zero in this specification.

(Results not shown, available upon request.) So at least within our sample of community banks (all with

small footprints to start with), geographic diversification influenced neither the impact of the financial crisis

on net new SME lending nor the strength of loan overhang or risk tolerance effects on net new SME lending.

Fourth, we tested whether and how our findings vary by bank equity ratios. While our results above

indicate that some banks (commercial focused banks) became less risk tolerant during the financial crisis—

that is, a drop in equity capital during the crisis resulted in an even larger reduction in new SME lending—

it would be instructive to know whether this effect was, say, weaker at low-capital banks that may be

experiencing moral hazard incentives. For these tests, we replaced COMM with the dummy variable

LOWEQ, which equals one for banks with EQ ≤ 8%.40 The results are displayed in Table 10. All else

equal, the financial crisis induced similar reductions in net new business lending at both low-equity and

high-equity banks: ∂NEW_BUS/∂CRS equals -0.0033 at the former and -0.0049 at the latter. The same-

sector overhang effect grew weaker for low-equity banks during the crisis (coefficient on

BUS*CRS*LOWEQ > 0), a result that is consistent with risk-seeking behavior at poorly capitalized banks

(e.g., Merton 1977, Marcus 1984), but one that would require additional evidence before drawing a strong

conclusion. Cross-sector overhang effects for consumer loans are stronger at low-equity banks, consistent

with the predicted risk tolerance effect, while cross-sector overhang effects for real estate loans are

unchanged at low-equity banks. Given the relatively high liquidity of the real estate loans in our sample

(53% home mortgage and home equity loans), the latter result is consistent with the substitutability of equity

and liquid loans that lies at the center of our theory model. Our credit rationing result is robust to bank

equity: during the crisis, neither high-equity nor low-equity banks exhibit business lending sensitivity to

40 The median value of EQ is 0.0864, so LOWEQ equals one for slightly less than half of the banks in the sample. We also tried using thresholds lower than 8% to define LOWEQ, which produced robust results. A variety of regulatory capital minimums prevent bank equity ratios from falling very low for any length of time—hence, the distribution of EQ is bunched up tightly between 6% and 8% (i.e., the distribution of EQ is highly skewed upward), so using thresholds between 6% and 8% to define LOWEQ does not meaningfully differentiate across subset of banks.

44

RAR. The risk tolerance effect is substantially stronger at low-capital banks (coefficient on EQ*LOWEQ =

0.0719) but this effect disappears during the crisis (compare ∂NEW_BUS/∂EQ in columns 4 and 5). The

former result sensibly indicates that an equity capital shock will have a relatively bigger effect on lending

at capital-deficient banks. The latter result likely indicates that any net new capital raised by or otherwise

injected into low-capital banks during the crisis years was absorbed rather than used to back new SME

lending, consistent with pressure from bank supervisors to increase risk-weighted capital ratios.

Finally, we investigate whether banks exhibit consistent changes in business lending behavior

across different recessions. One would expect to find less pronounced changes in bank lending behavior

during the relatively mild 2001 recession than during the financial crisis. We test this conjecture by

estimating our model using only the pre-crisis data subsample (1991:Q4 to 2007:Q3) and replacing the CRS

variable with the dummy variable REC2001, which equals one for all observations from 2000:Q2 through

2003:Q2.41 The results, displayed in Table 11, provide little evidence that the 2001 recession interrupted

community banks’ supply of small business credit or otherwise influenced their lending behaviors. The

baseline theoretical results (see column 2) for loan overhang, risk tolerance and risk-adjusted loan return

are similar in sign, magnitude and statistical significance as those in Table 8. Moreover, loan illiquidity

still results in enhanced same-sector overhang and risk tolerance effects (see the coefficients on

BUS*COMM and EQ*COMM). But ∂NEW_BUS/∂REC2001 is not statistically significant, and only none

of the coefficients on variables that include REC2001 are statistically significant.

8. Conclusion and discussion

Small businesses are especially reliant on bank finance. But during recessions, credit can become

less available to small firms if bank lenders—who face declining loan quality, potential or actual reductions

in the equity capital necessary to back new loans, and illiquid asset markets that make it difficult to raise

funds via loan sales—take risk-averse actions to conserve equity capital. Such behavior by banks can

41 As with the financial crisis, we based these beginning and end dates based on small banks’ response to the ‘demand for business lending’ question in the periodic Federal Reserve Surveys of Senior Lending Officers.

45

exacerbate economic downturns by restricting credit to job-creating small businesses. We estimate a

structural econometric model of new business lending by small U.S. banks between 1991 and 2010, paying

special attention to the impact of the global financial crisis on small business credit supply in 2007-2010.

The empirical loan supply equation is derived from a model of portfolio lending in which lenders are risk

averse, originate and hold illiquid loans, and have costly external capital (Froot, Scharfstein and Stein 1993,

Froot and Stein 1998, Gron and Winton 2001), conditions which are especially descriptive of community

bank lenders. The model predicts that a bank’s small business lending decisions will be constrained by the

composition of the preexisting (overhanging) loans on its balance sheet, its available equity capital

balances, and the expected returns to making new business loans. Thus, our study not only extends the

literature on small business credit supply during the global financial crisis to include the U.S. experience,

but also provides a micro-theoretic framework to better understand the results from studies of small business

lending in Europe during the financial crisis (e.g., Popov and Udell 2010; Jimenez, Ogena, Peydro and

Saurina 2012; Cotugno, Monferra and Sampagnaro 2012).

Our primary result is consistent with the prior studies of small business lending in Europe. On

average, during the financial crisis U.S. community banks reduced by a non-trivial amount their supply of

credit to SMEs. This suggests that there are important similarities in U.S. and European SME lending

markets, despite substantial institutional and regulatory differences across these two sets of markets. But

we also identify a small segment of U.S. community banks (about 13% of our data)—those that persistently

practiced a strategy of making illiquid loans to commercial entities—for which the supply of credit

increased during the crisis. The latter result (evocative of the exclusive relationship finding of Cotugno,

Monferra and Sampagnaro 2012) suggests a difference in the intensity of business borrower-bank lender

relationships between these two sets of small banks, and highlights an important feature of a strong banking

relationship: credit is made available when it is most needed.

Our empirical results offer strong support for the predictions of our theory. During the pre-crisis

period (1991-2007:Q3), small U.S. banks allocated additional capital to business loans when the expected

returns to making those loans was high, when they had plentiful amounts of equity capital, and when the

46

expected returns on business loans covaried negatively with the preexisting illiquid (overhanging) loans in

their portfolios. During the financial crisis (2007:Q4-2010), new business lending became increasingly

sensitive to overhanging loans and equity capital balances, implying that banks became less tolerant of risk

during the downturn as overhanging loans became less liquid and external equity capital became more

expensive. We also find evidence of lending inefficiencies. Prior to the crisis, new small business lending

was strongly and positively associated with the expected return on small business loans, indicative of a loan

supply relationship. But during the crisis, new lending became insensitive (perfectly inelastic) to expected

loan return, indicative of credit rationing behavior by banks.

Overall, our findings for small bank business lending in the U.S. are consistent with portfolio

management in which current credit is allocated efficiently and scarce capital is conserved for future

profitable lending opportunities. Some borrowers will face tighter credit supply during short-run periods

of heightened bank risk aversion, when lender balance sheets exhibit an unusually high amount of risk

overhang and/or when banks experience internal or external pressure to increase their equity capital. But

in the long run, a risk-averse lender is more likely to be around to provide funding and other financial

services, thus making bank-borrower relationships possible.

It is worth wondering about how the small and relatively less sophisticated banks in our data have

been able to manage loan portfolio risk with the degree of efficiency suggested by our estimates. Plainly

stated, these banks probably do not make calculations on cross-sector loan performance covariances, but

they may approximate modern portfolio theory by using rules of thumb or crude risk management tools.

One such tool is loan concentration limits, which can mimic modern portfolio management when it restricts

banks from making new loans which covary strongly and positively with preexisting portfolio loans. Of

course, binding concentration limits will cause banks to forego risk-return gains when they restrict banks

from making new loans that covary negatively with preexisting portfolio loans. And clearly, the secular

build-up of real estate loans in banks portfolios (see Figure 1) indicates that the typical small bank did not

tightly apply concentration limits at the loan-sector level, often to its detriment.

Our findings suggest that bank loan supply has pro-cyclical tendencies, and these tendencies may

47

exacerbate macro-economic cycles. As bank lending becomes more profitable due to an economic or

sector-specific expansion, banks’ equity capital, lending capacity, and tolerance for risk will all increase.

The resulting increase in loan supply will be further enhanced by the relatively liquid nature of well-

performing loans. As the expansion continues, at some point banks will need to compete for new business

by providing loans to riskier borrowers and/or by providing loans at lower interest rates. When the

expansion ends—as a result of banks’ behavioral excesses or exogenous economic shocks—defaulting

loans will reduce bank capital, lending capacity, and risk tolerance. The resulting decrease in loan supply

will be further reduced, as highlighted in our data, by the effects of loan overhang as loans become more

risky and less liquid. These effects will be moderated if banks hold precautionary balances of liquid assets

and/or a significant portion of their loans in sectors whose shocks are less positively correlated with the

sector-specific downturn. As such, our findings suggest that the pro-cyclical capital buffers included in

Basel III will result in social welfare gains.

Our findings also have implications for bank solvency policy during severe economic downturns.

In response to the financial crisis, the Troubled Asset Relief Program (TARP) and related programs injected

nearly $600 billion of equity capital into over 900 financial institutions, the majority of which were

commercial banks.42 The objective was two-fold: to stabilize systemically important banks, and to replenish

the industry capital base so that banks would increase lending. With respect to the latter objective, our

robustness tests suggest that government equity capital purchase programs would be most effective at

already well-capitalized banks, where it would have increased these banks’ tolerance for taking new lending

risks during a severe recession, but ineffective at poorly capitalized banks, where the funds would have

simply been retained in order to increase lagging capital ratios.

With regard to the banks in our data set, a caveat is in order. We have focused on the behavior of

small and relatively diversified banks; large banks or more specialized banks may behave differently. For

example, large banks may be able to use alternative risk management techniques to reduce overhang effects.

42 The U.S. Treasury has not yet reported a detailed list of all recipients of TARP funds. These numbers can be found at http://projects.propublica.org/bailout/list/index.

48

Similarly, specialized banks’ loan performance may be better than that of diversified banks due to the

expertise derived from greater lending focus, which might lead to improved risk-bearing ability in

downturns. Alternatively, their lack of diversification may make them behave in a more pro-cyclical way,

exacerbating the effects we have found here.

49

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Table 1 Correspondence between theoretical variables and regression variables and definitions of regression

variables.

Variable name in theory model

Corresponding regression

variable name Description of regression variable

Li,t-1 BUS RE

CON

Outstanding loan stock: The loan stock in sector i at the end of period t-1, normalized by bank assets. Call report codes: real estate loans = RCFD1410; business loans = RCFD1766; consumer loans = RCFD2011 + RCFDB539; assets = RCFD2170.

NLSi,t

NEW_BUS NEW_RE

NEW_CON

New lending: The change in sector i loan stock during period t (from the end of period t-1 through the end of period t), plus net loan charge-offs (charge-offs less recoveries) during the period, normalized by bank assets at the beginning of the period. Additional call report codes: net real estate charge-offs = RIAD4613 - RIAD4616; net business charge-offs = RIAD4638 - RIAD4608; net consumer charge-offs = RIADB516 - RIADB517.

Gt-1 EQ

Risk tolerance: Bank equity capital divided by bank assets at end of period t-1. Additional call report codes: equity = RCFD3210.

(pi,t - µi,t)/σii RAR

Risk-adjusted return: Expected return for business loans in period t divided by the Variance of expected return for business loans divided by 100, where: Expected return is bank-specific interest revenue from business loans, divided by accruing business loans (loan stock minus non-accruing loans) during period t-1, multiplied by the historical percentage of performing business loans in the state (twenty-quarter lagging average), minus the bank’s opportunity cost of funds (interest payments on deposits during the period divided by the average level of deposits during the period). Variance of expected return is the variance over the preceding twenty-quarter period of the quarterly average of bank-specific expected returns on business loans in the state in which the bank’s main office is located. Additional call report codes: interest revenues from business loans = RIAD4012; non-accruing business loans = RCON1608; nonperforming business loans = RCON1607 + RCON1608; deposit interest expense = RIAD4170 + RIAD4180; deposits = RCON2215 + RCON2385 + RCONB993 + RCONB995.

55

Table 2 Descriptive Statistics. Small U.S. commercial banks between 1991:Q4 and 2010:Q4. Unbalanced panel

includes 66,798 quarterly observations from 3,210 separate banks.

N Mean Median Std Dev Min Max Number of quarters per bank -- 39.6 37.0 20.2 5 88 Bank assets (millions of 2010 $) 66,798 212.6 110.3 267.1 18.1 1975.2 Structural variables NEW_BUS 66,798 0.0027 0.0018 0.0111 -0.1448 0.1008 NEW_RE 66,798 0.0089 0.0068 0.0169 -0.0602 0.1549 NEW_CON 66,798 0.0012 0.0005 0.0079 -0.1684 0.1868 BUS 66,798 0.1183 0.1034 0.0635 0.0154 0.5420 RE 66,798 0.3387 0.3375 0.1093 0.0278 0.7216 CON 66,798 0.1019 0.0838 0.0631 0.0160 0.7037 EQ 66,798 0.0921 0.0864 0.0250 0.0010 0.3709 RAR 66,798 0.8139 0.3115 1.5929 -0.0624 12.4435 Demand Shifters (DS) Per Capita Income 66,798 26.2944 25.2525 6.0509 14.1412 56.8060 %∆Unemployment 66,798 0.0044 -0.0074 0.1312 -0.5031 0.8057 Unemployment Rate 66,798 5.3150 5.1000 1.5380 1.7000 14.3000 Instruments Personal Income Tax Rate 66,798 0.1466 0.1514 0.0152 0.1021 0.1822 Traffic Fatalities 66,798 0.0003 0.0002 0.0001 0.0001 0.0006 Rental Vacancies 66,798 8.7295 8.4000 2.7065 2.7000 18.1000 Unexpected Snowfall 66,798 0.2367 0 0.8167 -6.2385 15.6 Variables capturing exogenous variation COMM 66,798 0.1253 0 0.331 0 1 CRS 66,798 0.0522 0 0.2224 0 1 SUB_S 31,380 0.255 0 0.4359 0 1 TAX CHANGE 31,380 0.0000 0 0.0002 -0.0113 0.0147 TAXINC 31,380 0.0104 0 0.1014 0 1 Variables used in robustness testing LOWEQ 66,798 0.3474 0 0.4761 0 1 RAR_Realized 66,798 1.2654 1.0284 1.0452 -2.5889 8.6441 RAR_Foresight 66,798 1.5841 1.1967 1.2402 -0.2973 10.1583 REC2001 63,313 0.1681 0 0.3739 0 1

56

Table 3 Comparing characteristics of bank sample (non-specialist community banks) to bank population (all community banks). Data on credit risk and loan liquidity for sample banks (first column) and all banks with less than $2 billion in assets (second column). The mean values for the loan charge-off ratios reported in item 1 are computed using bank-quarter observations during the 1991-2010 sample period for the three loan variables BUS, RE and CON. The mean aggregate values for the loans sold or securitized ratios reported in item 2 are the average of the quarterly sample aggregate ratios, and are based on the sum of two call report items: “Outstanding principal balances of assets sold and securitized by the reporting banks with serving retained or with recourse or other seller-provided credit enhancements” plus “Assets sold withy recourse of other seller-provided credit enhancements and not securitized by the reporting bank.”

Sample banks

Specialist and non-specialist banks

community banks 1. Loans charged-off, % of total loans (means of bank-quarter observations): BUS 0.65% 0.97% RE 0.10% 0.18% CON 0.51% 0.62% 2. Loans sold or securitized for which banks have existing recourse exposure, % of total loans (means of quarterly aggregate ratios): BUS 0.07% 0.19% RE (excluding commerical real estate) 1.29% 3.25%

CON 1.01% 0.45%

57

Table 4: Expected Profit Covariances Number and percentage of banks for which the expected quarterly returns from Business Loans (BUS) covary positively with the expected quarterly returns from Real Estate Loans (RE) or Consumer Loans (CON) during the 1991:Q4 to 2010:Q4 sample period. ***, ** and * indicate different from 50% at the 1%, 5% and 10% levels of significance.

Cov(BUS, RE) Cov(BUS, CON) # of positive covariances 1401 1481 % of positive covariances 43.6%*** 46.1%*** Number of banks 3,210 3,210

58

Table 5 Loan portfolio composition, expressed as a percentage of total loans. The commercial focus dummy (COMM) equals 1 if a bank's commercial loans share is in the upper quartile, and its noncommercial loans share is in the bottom quartile, of the quarterly sample distribution persistently for the previous ten quarters.

(1) (2) (3)

full sample COMM=0 COMM=1

Business loans (BUS) 21.5% 19.5% 32.8% Consumer loans (CON) 18.3% 19.5% 11.7% Real estate loans (RE) 60.2% 61.0% 55.5% Components of real estate loans: Residential mortgage 29.7% 31.8% 14.6% HELOC 2.4% 2.5% 1.9% Construction & land development 6.0% 5.5% 9.4% Nonfarm, nonresidental loans 20.2% 19.0% 28.5%

Number of observations 66,798 58,430 8,368

59

Table 6 Estimation of equation (5) for full 1991:Q4-2010:Q4 sample. ***, ** and * indicates statistical

differences from zero at the 1%, 5% and 10% levels of significance, respectively.

(1) (2) (3) (4) (5) (6)

Model: Panel OLS IV-2SLS IV-2SLS Panel OLS IV-2SLS IV-2SLS

NEW_RE -0.0513*** -0.0917 -0.2580 -0.0516*** -0.0895 -0.3090**

(0.0027) (0.1414) (0.1660) (0.0027) (0.1500) (0.1313)

NEW_CON -0.0023 0.5705* 0.2277 -0.0024 0.4724 0.2803

(0.0057) (0.2936) (0.3351) (0.0057) (0.3218) (0.3285)

RE -0.0022** -0.0015 -0.0040 -0.0022** -0.0017 -0.0054**

(0.0009) (0.0022) (0.0026) (0.0009) (0.0024) (0.0023)

BUS -0.0365*** -0.0370*** -0.0300*** -0.0366*** -0.0369*** -0.0290***

(0.0015) (0.0035) (0.0050) (0.0015) (0.0037) (0.0044)

CON 0.0047*** 0.0097*** 0.0073** 0.0048*** 0.0089*** 0.0044

(0.0014) (0.0035) (0.0036) (0.0014) (0.0034) (0.0038)

EQ 0.0142*** 0.0137** 0.0103* 0.0147*** 0.0141** 0.0109*

(0.0037) (0.0057) (0.0061) (0.0037) (0.0055) (0.0062)

RAR 0.00018*** 0.00019** 0.00239** 0.00017** 0.00017* 0.00219***

(0.00007) (0.00009) (0.00107) (0.00007) (0.00009) (0.00103)

Per Capita Income 0.0004*** 0.0002 0.0003** 0.0002** 0.0002 0.0004***

(0.0001) (0.0002) (0.0002) (0.0001) (0.0002) (0.0001)

%∆Unemployment -0.0034*** -0.0036*** -0.0042*** -0.0020*** -0.0021*** -0.0025***

(0.0006) (0.0009) (0.0010) (0.0005) (0.0006) (0.0007)

Unemployment Rate -0.0008*** -0.0008*** -0.0006** -0.0001 -0.0001 0.0001

(0.0002) (0.0003) (0.0003) (0.0001) (0.0001) (0.0001)

Bank Fixed Effects Yes Yes Yes Yes Yes Yes

Quarter Fixed Effects Yes Yes Yes Yes Yes Yes

Clustering (Bank) No Yes Yes No Yes Yes

Fitted demand shifters Yes Yes Yes No No No

F-test for demand shifters 21.75 36.79 38.43 10.45 12.17 20.29 Instruments for NEW_RE and NEW_CON

No Yes Yes No Yes Yes

Instruments for RAR No No Yes No No Yes

Underidentification (p-value) 0.00 0.00 0.00 0.00

Overidentification (p-value) 0.10 0.23 0.10 0.28 Weak Identification (F=7.56 at 10% maximal IV relative bias)

7.14 8.05 6.77 6.64

Bank-Quarter observations 66,798 66,798 66,798 66,798 66,798 66,798

Banks 3,210 3,210 3,210 3,210 3,210 3,210

60

Table 7 Testing for risk overhang effects using exogenous variation in bank organization form and state tax law. SUB_S is a dummy equal to one for banks with subchapter S status. TAXINC is a dummy equal to one during each of the first four quarters following an increase in state personal tax rates in the bank’s home state. The baseline 2SLS-IV model of equation (5) is augmented to include interactions of SUB_S and TAXINC with the main variables of interest as well as a control variable (TAX CHANGE) for changes in state level personal income tax rates. Model is estimated for a subsample of our main database from 1998:Q1 to 2010:Q4. ***,**, and * indicate statistical differences from zero at the 1%, 5%, and 10% levels of significance, respectively.

(1) (2) (3) (4) (5)

Estimated partial derivatives evaluated for different values of the SUB_S and TAXINC dummy variables:

SUB_S = 0 SUB_S = 1 SUB_S = 0 SUB_S = 1

TAXINC = 0 TAXINC = 0 TAXINC = 1 TAXINC = 1 NEW_RE 0.0972 (0.1515) NEW_CON 1.0189** (0.4520) RE 0.0011 0.0011 0.0029 0.0067 0.0305** (0.0044) (0.0044) (0.0056) (0.0088) (0.0137) RE*SUB_S 0.0018 (0.0038) RE*TAXINC 0.0056 (0.0071) RE*SUB_S*TAXINC 0.0220** (0.0110) BUS -0.0428*** -0.0428*** -0.0717*** -0.0442*** -0.1355*** (0.0062) (0.0062) (0.0071) (0.0136) (0.0253) BUS*SUB_S -0.0289*** (0.0075) BUS*TAXINC -0.0014 (0.0124) BUS*SUB_S*TAXINC -0.0624** (0.0257) CON 0.0204*** 0.0204*** 0.0234* 0.0463** 0.1066** (0.0078) (0.0078) (0.0137) (0.0193) (0.0511) CON*SUB_S 0.0030 (0.0113) CON*TAXINC 0.0259 (0.0162) CON*SUB_S*TAXINC 0.0573** (0.0286)

61

EQ 0.0240** 0.0240** -0.0040 0.0181 0.0382 (0.0098) (0.0098) (0.0149) (0.0288) (0.0313) EQ*SUB_S -0.0280* (0.0152) EQ*TAXINC -0.0058 (0.0274) EQ*SUB_S*TAXINC 0.0481 (0.0376) RAR 0.00049** 0.00049** 0.00042 0.00065 -0.00011 (0.00024) (0.00024) (0.00032) (0.00044) (0.00092) RAR*SUB_S -0.0001 (0.0002) RAR*TAXINC 0.0002 (0.0004) RAR*SUB_S*TAXINC -0.0007 (0.0009) SUB_S 0.0044* (0.0025) TAXINC -0.0031 (0.0048)

TAX CHANGE 0.0453

(0.2892)

Bank Fixed Effects Yes Quarter Fixed Effects Yes Clustering (Bank) Yes

Fitted demand shifters Yes F-Test for demand shifters 9.40 Instruments for NEW_RE, NEW_CON and RAR

Yes

Underidentification (p-value) 0.00 Overidentification (p-value) 0.21

Weak Identification (F=7.56 at 10% level)

7.40

Bank-Quarter Observations 31,380

Banks 1,918

62

Table 8 Testing for risk overhang effects using exogenous variation in bank business models and macro-economic regimes. COMM is a dummy equal to one for banks with commercial lending focus, where COMM equals 1 if a bank's commercial loans share is in the upper quartile, and its noncommercial loans share is in the bottom quartile, of the quarterly sample distribution persistently for the previous ten quarters. CRS is a dummy equal to one for bank-quarter observations between 2007:Q4 and 2010:Q4. The baseline 2SLS-IV model of equation (5) is augmented to include interactions of COMM and CRS with the main variables of interest. Model is estimated for the full 1991:Q4 to 2010:Q4 data sample. ***, ** and * indicates statistical differences from zero at the 1%, 5% and 10% levels of significance, respectively.

(1) (2) (3) (4) (5)

Estimated partial derivatives evaluated for different values of the CRS and COMM dummy variables:

CRS = 0 CRS = 1 CRS = 0 CRS = 1

COMM = 0 COMM = 0 COMM = 1 COMM = 1

NEW_RE -0.0446 (0.1376) NEW_CON 0.3343 (0.2349) RE -0.0021 -0.0021 -0.0001 -0.0088** -0.0133 (0.0021) (0.0021) (0.0037) (0.0036) (0.0171) RE*CRS 0.0020 (0.0026) RE*COMM -0.0067** (0.0029) RE*CRS*COMM -0.0065 (0.0160) BUS -0.0336*** -0.0336*** -0.0525*** -0.0477*** -0.0687*** (0.0036) (0.0036) (0.0073) (0.0054) (0.0101) BUS*CRS -0.0190*** (0.0065) BUS*COMM -0.0141*** (0.0053) BUS*CRS*COMM -0.0021 (0.0118) CON 0.0078*** 0.0078*** 0.0094 0.0255** 0.2249*** (0.0028) (0.0028) (0.0070) (0.0101) (0.0866) CON*CRS 0.0016 (0.0057) CON*COMM 0.0177* (0.0104) CON*CRS*COMM 0.1978** (0.0876)

63

EQ 0.0080* 0.0080* 0.0213** 0.0494*** 0.1243*** (0.0058) (0.0058) (0.0102) (0.0126) (0.0352) EQ*CRS 0.0133 (0.0097) EQ*COMM 0.0414*** (0.0129) EQ*CRS*COMM 0.0616* (0.0338) RAR 0.00042** 0.00042** 0.00028 0.00060*** -0.00480

(0.00021) (0.00021) (0.00030) (0.00021) (0.00294)

RAR*CRS -0.0001 (0.0001) RAR*COMM 0.0002 (0.0001) RAR*CRS*COMM -0.0053** (0.0023) COMM -0.0012 (0.0017) CRS -0.0031 (0.0021) Bank Fixed Effects Yes Quarter Fixed Effects Yes Clustering (Bank) Yes

Fitted demand shifters Yes F-Test for demand shifters 8.36 Instruments for NEW_RE, NEW_CON and RAR

Yes

Underidentification (p-value) 0.00 Overidentification (p-value) 0.19 Weak Identification (F=7.56 at 10% maximal IV relative bias) 9.86

∂NEW_BUS/∂CRS(COMM=0) -0.0033** ∂NEW_BUS/∂CRS(COMM=1) 0.0157*** Bank-Quarter Observations 66,798

Banks 3,210

64

Table 9 Estimating the impact of the financial crisis (CRS) on net new business lending. The values displayed in the table are based on an augmented version of the model displayed in Table 8 in which the single CRS dummy is replaced by a set of three single-year dummy variables. The cells display the values of the derivative ∂BUS_NEW/∂CRS evaluated in each of the three years of the crisis (columns 1, 2 and 3), for either value of the strategic lending focus variable COMM (rows 1 and 2), and otherwise at the means of the data. COMM equals 1 if a bank's commercial loans share is in the upper quartile, and its noncommercial loans share is in the bottom quartile, of the quarterly sample distribution persistently for the previous ten quarters. ***, ** and * indicates statistical differences from zero at the 1%, 5% and 10% levels of significance, respectively.

(1) (2) (3)

∂NEW_BUS/∂CRS

1st crisis year (2007:Q4-2008:Q4)

2nd crisis year (2009:Q1-2009:Q4)

3rd crisis year (2010:Q1-2010:Q4)

evaluated at COMM = 0 (reflects net new business lending at 58,430 quarterly observations of banks with retail lending focus)

-0.0038** * -0.0053*** -0.0038**

evaluated at COMM = 1 (reflects net new business lending at 8,368 quarterly observations of banks with commercial lending focus)

0.0201*** -0.0079 0.0105

65

Table 10 Testing for the effects of equity ratios on risk overhang effects. 2SLS-IV estimation of equation (5), augmented to include a full set of differences-in-differences terms from equation (6), for the entire 1991:Q4 to 2010:Q4 data sample. The crisis dummy (CRS) equals 1 for bank-quarter observations between 2007:Q4 and 2010:Q4. The low equity (LOWEQ) equals 1 if a bank's equity-to-assets ratio is less than 8%. ***, ** and * indicates statistical differences from zero at the 1%, 5% and 10% levels of significance, respectively.

(1) (2) (3) (4) (5)

Estimated partial derivatives evaluated for different

values of the CRS and LOW dummy variables:

CRS = 0 CRS = 1 CRS = 0 CRS = 1

LOWEQ=0 LOWEQ=0 LOWEQ=1 LOWEQ=1

NEW_RE -0.0498

(0.1365)

NEW_CON 0.2989

(0.2409)

RE -0.0032 -0.0032 -0.0006 -0.0026 0.0019 (0.0021) (0.0021) (0.0035) (0.0026) (0.0054) RE*CRS 0.0027 (0.0026) RE*LOWEQ 0.0006 (0.0017) RE*CRS*LOWEQ 0.0019 (0.0042) BUS -0.0357*** -0.0357*** -0.0589*** -0.0379*** -0.0383*** (0.0036) (0.0036) (0.0075) (0.0040) (0.0109) BUS*CRS -0.0232*** (0.0069) BUS*LOWEQ -0.0021 (0.0032) BUS*CRS*LOWEQ 0.0228** (0.0113) CON 0.0067** 0.0067** 0.0073 0.0112*** 0.0247** (0.0030) (0.0030) (0.0069) (0.0031) (0.0118) CON*CRS 0.0006 (0.0056) CON*LOWEQ 0.0045** (0.0021) CON*CRS*LOWEQ 0.0129 (0.0105) EQ 0.0093 0.0093 0.0269** 0.0812*** 0.0276

66

(0.0063) (0.0063) (0.0115) (0.0187) (0.0491) EQ*CRS 0.0176* (0.0103) EQ*LOWEQ 0.0719*** (0.0202) EQ*CRS*LOWEQ -0.0712* (0.0429) RAR 0.00037* 0.00037* 0.00010 0.00048*** 0.00071

(0.00021) (0.00021) (0.00031) (0.00020) (0.00070)

RAR*CRS -0.0003

(0.0002)

RAR*LOWEQ 0.0001

(0.0001)

RAR*CRS*LOWEQ 0.0005

(0.0007)

LOWEQ -0.0057***

(0.0016)

CRS -0.0030

(-0.0021)

Bank Fixed Effects Yes Quarter Fixed Effects Yes Clustering (Bank) Yes

Fitted demand shifters Yes F-Test for demand shifters 9.24 Instruments for NEW_RE, NEW_CON and RAR

Yes

Underidentification (p-value) 0.00 Overidentification (p-value) 0.29 Weak Identification (F=7.56 at 10% level)

9.99

∂NEW_BUS/∂CRS(LOWEQ=0) -0.0033**

∂NEW_BUS/∂CRS(LOWEQ=1) -0.0049**

Bank-Quarter Observations 66,798

Banks 3,210

67

Table 11 Testing for risk overhang effects during the 2001 recession. 2SLS-IV estimation of equation ( 5), augmented to include a full set of differences-in-differences terms from equation ( 6), for the pre-crisis subsample 1991:Q4 to 2007:Q3 data sample. The crisis dummy (REC2001) equals 1 for bank-quarter observations between 2000:Q2 and 2003:Q2. The commercial focus dummy (COMM) equals 1 if a bank's commercial loans share is in the upper quartile, and its noncommercial loans share is in the bottom quartile, of the quarterly sample distribution persistently for the previous ten quarters. ***, ** and * indicates statistical differences from zero at the 1%, 5% and 10% levels of significance, respectively.

(1) (2) (3) (4) (5)

Estimated partial derivatives evaluated for different

values of the REC2001 and COMM dummy variables:

REC2001=0 REC2001=1 REC2001=0 REC2001=1

COMM = 0 COMM = 0 COMM = 1 COMM = 1

NEW_RE -0.1017 (0.1775) NEW_CON 0.3317 (0.2472) RE -0.0029 -0.0029 -0.0049 -0.0087** -0.0152*** (0.0023) (0.0023) (0.0031) (0.0043) (0.0049) RE*REC2001 -0.0020 (0.0017) RE*COMM -0.0059* (0.0033) RE*REC2001*COMM -0.0045 (0.0040) BUS -0.0365*** -0.0365*** -0.0317*** -0.0492*** -0.0482*** (0.0038) (0.0038) (0.0052) (0.0056) (0.0081) BUS*REC2001 0.0047 (0.0036) BUS*COMM -0.0127** (0.0057) BUS*REC2001*COMM -0.0037 (0.0083) CON 0.0092*** 0.0092*** 0.0070 0.0271** 0.0276 (0.0031) (0.0031) (0.0059) (0.0110) (0.0203) CON*REC2001 -0.0021 (0.0040) CON*COMM 0.0180 (0.0114) CON*REC2001*COMM 0.0026 (0.0208)

68

EQ 0.0100 0.0100 -0.0011 0.0494*** 0.0461*** (0.0063) (0.0063) (0.0083) (0.0135) (0.0159) EQ*REC2001 -0.0110 (0.0084) EQ*COMM 0.0395*** (0.0137) EQ*REC2001*COMM 0.0076 (0.0152) RAR 0.00043** 0.00043** 0.00028 0.00057** 0.00084***

(0.00022) (0.00022) (0.00024) (0.00023) (0.00032)

RAR*REC2001 -0.0001 (0.0001) RAR*COMM 0.0001 (0.0001) RAR*REC2001*COMM 0.0004 (0.0003) COMM -0.0015 (0.0018) REC2001 0.0024 (0.0015) Bank Fixed Effects Yes Quarter Fixed Effects Yes Clustering (Bank) Yes

Fitted demand shifters Yes F-Test for demand shifters 7.57 Instruments for NEW_RE, NEW_CON and RAR

Yes

Underidentification (p-value) 0.00 Overidentification (p-value) 0.49 Weak Identification (F=7.56 at 10% level)

8.41

∂NEW_BUS/∂CRS(COMM=0) -0.0002

∂NEW_BUS/∂CRS(COMM=1) 0.0001

Bank-Quarter Observations 63,313

Banks 3,192

69

Figure 1

Three major categories of commercial bank loans, as defined in the call reports, for U.S. commercial banks with assets less than $2 billion (2010 dollars) between 1987 and 2010. The data are quarterly

cross-sectional means, expressed as a percentage of bank assets.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

1986 1991 1996 2001 2006 2011

Total Real Estate C&I Consumer (Exc. Credit Card)

70

Figure 2

Kaplan-Meier estimates. Hazard probability that a commercial focus bank (COM=1) will abandon its strategy after having practiced it for a given number of consecutive quarters (horizontal axis).

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

1 3 5 7 9 11 13 15 17 19 21 23 25 27 30 32 34 37 42 45 51 53 65

Quarters

71

APPENDIX A First stage regression estimates associated with Table 6, column 4. Estimated using ordinary least squares (OLS), bank fixed effects, time fixed effects, and errors clustered at the bank level. The instrumental variables are in these regressions are observed each quarter for the state in which a bank has its headquarters and are defined as follows: Unexpected Snowfall is the deviation from the seasonal median averages in the state. Personal Income Tax Rate is the average federal plus state personal income tax rate in the state. Traffic Fatalities is the natural log of the number of traffic accident fatalities in the state. Rental Vacancies is the proportion of rental properties that are vacant in the state. ***, ** and * indicates statistical differences from zero at the 1%, 5% and 10% levels of significance, respectively. All variables are defined in Table 1.

APPENDIX Table A (1) (2) (3)

Dependent Variable: NEW_RE NEW_CON RAR RE -0.0129*** -0.0019** -0.12977 (0.0022) (0.0009) (0.2013) BUS 0.0151*** 0.0019 -1.7063*** (0.0038) (0.0017) (0.3014) CON 0.0030 -0.0085*** -0.0243 (0.0032) (0.0023) (0.2902) EQ -0.0071 0.0005 1.1051* (0.0085) (0.0040) (0.6684) Per Capita Income 0.0002 0.0002* -0.0136 (0.0027) (0.0001) (0.0189) %∆Unemployment -0.0023** 0.0002 -0.0456 (0.0009) (0.0004) (0.0353) Unemployment Rate -0.0012*** 0.0001 -0.0238 (0.0003) (0.0002) (0.0193) Unexpected Snowfall -0.0004*** 0.0001 0.0106** (0.0001) (0.0001) (0.0046) Rental Vacancies -0.0001 -0.0001*** -0.0254*** (0.0001) (0.0000) (0.0060) Personal Income Tax Rate 0.0641 -0.0771*** -15.9423*** (0.0537) (0.0261) (5.5780) Traffic Fatalities 9.2595 -2.2244 2994.16** * (5.5874) (2.6049) (643.61) Bank-Quarter observations 66,798 66,798 66,798 Banks 3,210 3,210 3,210

F-Statistics of Excluded Instruments 13.95 8.36 14.66

72

APPENDIX B Estimation of equation ( 5) using the three alternative definitions of RAR. In each definitions, the term “loans” always refers to business loans, the subscript i refers to the bank, the subscript t refers to the current quarter, the subscript t-1 refers to the loan stocks at the beginning of quarter t, and the subscript State refers to the state in which bank i is headquartered. Expected RAR is the definition that we use in our main tests. It assumes that bank management makes business lending decisions based on the average historical performance of business loans in its home state. (See Table 1 and the text for further details.):

����������,� =

�����������,��������������,���

∙ �%����������������� �!," #�$%&�'#(−��������������,����������������,�

��������������������� �!," #�$%&�'#

Realized RAR is the first alternative definition. It assumes that bank management makes business lending decisions based on the most recent performance of business loans in its own portfolio:

�����*����,� =

�����������,��������������,���

−�����ℎ����-����,�

�����,���−

��������������,����������������,�

��������������������� �!," #�$%&�'#

Foresight RAR is the alternative definition. It assumes that bank management has perfect foresight, i.e., its business lending decisions appear to be based on the future outcomes of its business loans:

�������ℎ���,� =

�����������,������,���

−��������������,����������������,�

��������������������� �!," #�$%&�'#

In the table that follows, the superscripts ***, ** and * indicate statistical differences from zero at the 1%, 5% and 10% levels of significance, respectively.

(over)

73

APPENDIX Table B Estimation of equation (5) for full 1991:Q4 to 2010:Q4 data sample. ***, ** and * indicates statistical

differences from zero at the 1%, 5% and 10% levels of significance, respectively.

Definition of RAR: Expected Realized Foresight

(1) (2) (3)

Model: IV-2SLS IV-2SLS IV-2SLS

NEW_RE -0.2580 -0.1078 -0.1963

(0.1660) (0.1816) (0.1681)

NEW_CON 0.2277 0.5506 0.4311

(0.3351) (0.3074) (0.2948)

RE -0.0040 -0.0019 -0.0040

(0.0026) (0.0029) (0.0028)

BUS -0.0300*** -0.0346*** -0.0247***

(0.0050) (0.0093) (0.0087)

CON 0.0073** 0.0095*** 0.0088***

(0.0036) (0.0036) (0.0034)

EQ 0.0103* 0.0135** 0.0118**

(0.0061) (0.0059) (0.0059)

RAR 0.00239** 0.00157 0.00219*

(0.00107) (0.00157) (0.00132)

Per Capita Income 0.0003** 0.0002 0.0002

(0.0002) (0.0002) (0.0002)

%∆Unemployment -0.0042*** -0.0037*** -0.0040***

(0.0010) (0.0010) (0.0009)

Unemployment Rate -0.0006** -0.0008** -0.0006**

(0.0003) (0.0003) (0.0003)

Bank Fixed Effects Yes Yes Yes Quarter Fixed Effects Yes Yes Yes Clustering (Bank) Yes Yes Yes

Fitted demand shifters Yes Yes Yes F-test for demand shifters 38.43 33.80 34.16 Instruments for NEW_RE and NEW_CON

Yes Yes Yes

Instruments for RAR Yes Yes Yes Underidentification (p-value) 0.00 0.00 0.00 Overidentification (p-value) 0.23 0.11 0.18 Weak Identification (F=7.56 at 10% level)

8.05 7.23 6.00

Bank-Quarter observations 66,798 66,798 66,798 Banks 3,210 3,210 3,210