Risk Overhang and Loan Portfolio Decisions: Small Business Loan Supply Before and During the Financial Crisis

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

Gokhan Torna, University of Kansas Andrew Winton, University of Minnesota

This draft: August 1, 2012

Short Abstract: We build a model of bank lending with capital market imperfections (asset illiquidity, costly equity capital) and risk-averse decision-makers, and estimate the model using data from portfolio-lending U.S. commercial banks between 1990 and 2010. The evidence is consistent with our theory. Prior to the financial crisis, new business lending declined with the illiquidity of pre-existing loans (loan overhang) and increased with stores of equity capital (risk aversion). As predicted, these phenomena grew stronger during the crisis as asset illiquidity, credit risk, and capital costs all increased. We also find evidence of business loan credit rationing during the crisis.

Portions of this paper are based on an unpublished manuscript titled “Risk Overhang and Loan Portfolio Decisions” (DeYoung, Gron and Winton 2006). 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. * Corresponding author: Robert DeYoung, University of Kansas School of Business, 1300 Sunnyside Avenue, Lawrence, KS 66045, rdeyoung@kuk.edu

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1. Introduction

Corporate finance theory suggests that when external finance is costly, value-maximizing

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

the expected returns from the investment opportunity in question, but also on their available

capital and that investment’s return covariance with the rest of their business. Such behavior

increases a firm’s expected profits by reducing the probability that the firm will forego a

valuable future investment opportunity—due to a lack of internal capital—when the return on the

investment does not justify the costs of raising additional external capital. In this paper, we

adapt this strain of finance theory to describe the investment decisions of bank lenders, and then

we test whether the predictions of the theory are consistent with actual business lending behavior

of U.S. commercial banks. Our empirical investigation focuses on small commercial banks,

which face the types of capital market imperfections assumed in the theory: their portfolios of

illiquid, informationally opaque small business loans lock-up internal equity capital and make

external equity capital finance expensive. Thus, in addition to providing a strong test of

corporate finance theory, we are able to test whether the investment behaviors described by that

theory caused a reduction and/or rationing of credit to U.S. small businesses during the global

financial crisis.

Commercial banks are an attractive subject for this research question for several reasons.

Because banks act as delegated monitors, they have private information about their loans that can

lead to lemons problems if they attempt to sell the loans. This illiquidity leads to testable

predictions: if old, illiquid loans create risk exposures that cannot be cheaply sold off, then banks

should take these exposures into account when deciding what additional loans should be made.

The degree of preexisting risk exposure—which we refer to here as “risk overhang” or “loan

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overhang”—will vary across different types of loans due to differences in their liquidity, and also

across time as economic circumstances vary. For example, during economic downturns both the

risk and illiquidity of loans should increase, and this will amplify any risk overhang effects

associated with preexisting portfolio loans. The recent financial crisis is a natural environment

for testing these phenomena, a period during which financial markets were illiquid, credit risk

was high, and bank equity capital was scarce and hence expensive.

To examine these conjectures, we derive a theory model of loan supply and then test the

model’s predictions using panel data from the financial statements of U.S. commercial banks.

Our model, which is based on Froot and Stein (1998), generates empirically tractable predictions

about the effects of loan overhang, expected loan returns, and competing lending opportunities

on banks’ supply of new loans, given banks’ current portfolio composition and capital. We test

these loan supply predictions for banks with assets less than $2 billion (2010 dollars) operating

in metropolitan and urban markets between 1990 and 2010. These banks make loans in three

main sectors (business, real estate and consumer) that differ in terms of loan liquidity, credit risk,

and performance co-variation, and we use two-stage least squares estimation to control for the

simultaneity of banks’ lending decisions across these different sectors. We pay special attention

to the 2007-2010 “crisis period” data—years in which macro-economic conditions were far more

severe than the mild downturns of the early 1990s and early 2000s—to test whether the business

loan supply predictions of our model are pro-cyclical.

Small, so-called “community banks” are a critical source of funding for small businesses,

chiefly due to the informational advantages inherent in the local focus of these banks.1 Because

1 Historically, small banks have generated disproportionate amounts of small business loans and have tended to use “relationship lending” techniques to generate this credit (Petersen and Rajan 1994, Berger, Saunders, Scalise, and Udell 1997, Berger, Miller, Petersen, Rajan and Stein 2005). More recently, large banks have begun to provide

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of this, small banks can be uniquely important for macro-economic growth: Berger, Hasan, and

Klapper (2004) find a positive empirical link between a large, healthy small banking sector and

macro-economic growth across 49 developed and developing nations. Crucially, data from small

banks provide an especially clean test of our theory. Because community banks lend to small,

privately-held firms that are opaque to public capital markets, the risk overhang associated with

their loans can be substantial, as these loans have no resale market and can be large relative to

the overall loan portfolio. Most community banks lack access to public funding markets; this

increases their cost of external financing, which in turn magnifies the consequences of all new

lending decisions. These banks are unlikely to use credit derivatives (CDS do not exist for small

business loans, and using existing CDS to hedge these loans would entail extreme basis risk), so

they must manage the risk of their loan portfolios by adjusting on-balance sheet loan

concentrations. And because bank managers are often placing their own or their family’s capital

at risk when making lending decisions (community banks are often owner-managed), risk-averse

lending behavior should be relatively free of potentially confounding principal-agent effects

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

Overall, our results indicate these banks make small business loan supply decisions

consistent with risk-averse value-maximizing behavior. First, 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 with expected returns that co-vary negatively with

business loans. Preexisting stocks of business loans (which tend to be less liquid and more

default-prone than consumer or real estate loans) generate the strongest risk overhang effects. In

increasing amounts of small business loans (Berger, Rosen, and Udell 2001, Petersen and Rajan 2002) although the cyclical implications of this for small business loan supply are not yet fully understood.

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general, loan overhang effects grew stronger during the financial crisis, consistent with

reductions in loan liquidity and lender risk tolerance during a downturn. Second, our results

confirm that we are estimating a supply relationship. Throughout most of our twenty year

sample period, new business lending increased with the expected return from these loans.

However, we are unable to find this positive relationship during the financial crisis, which

implies that new business loan supply grew inelastic during the crisis and suggests that banks

may have been rationing credit to small businesses. Third, the size of equity capital cushions

influences both new loan supply decisions and the degree to which loan overhang influences

these decisions. During normal times, reductions in bank capital ratios are associated with a shift

in new loan supply away from business loans and toward loan categories with historically lower

levels of default risk, a pattern that implies increased risk aversion in lending by banks.

Consistent with this, we find that reductions in capital are also associated with stronger loan

overhang effects. During the crisis period, however, the implied link between equity capital and

risk-averse lending behavior disappears for low-capital banks, consistent with the long

established literature (e.g., Merton 1977, Marcus 1984) on risk-seeking behavior at poorly

capitalized banks.

That these findings are generated using data from U.S. banks is especially important. In

the U.S., about two-fifths of all small businesses obtain some form of credit from a commercial

bank and, as previously noted, these loans come disproportionately from small banks.2 But the

lion’s share of extant knowledge on the behavior of small business lenders during economic

downturns comes from European markets where loan-level data are more plentiful. While our

2 Based on data from the Federal Reserve Survey of Consumer Finances reported in DeYoung, Hunter, and Udell (2004), and the Federal Reserve Survey of Small Business Finances reported in Bitler, Robb, and Wolken (2001), respectively.

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results confirm the central finding of those studies—i.e., that supply-side phenomena are the

predominant drivers of reduced small business lending activity during recessions—we also

extend this body of knowledge by empirically identifying the meta-drivers of small business

lender behavior (asset illiquidity, risk overhang, risk aversion) and showing that these forces

vary in strength across the business cycle. Understanding that portfolio lenders allocate their

capital in a risk-averse fashion has important ramifications for small businesses. 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. But 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.

More generally, our findings are consistent with models of pro-cyclical bank lending

driven by internal bank behavior (e.g., Rajan 1994; Berger and Udell 2004; Ruckes 2004).

During an economic expansion, demand for bank credit is high and business profitability is good,

resulting in profitable loans, increasing bank capital, and an expanding credit environment in

which banks lend more at lower rates as they compete for business. But as the expansion

inevitably ends, business profitability will decline, resulting in delinquent loan payments or

outright default, declining bank capital, and a tighter credit environment as banks make fewer

loans at higher rates. We find that risk overhang effects are themselves pro-cyclical at banks,

working to decrease small business loan supply during economic downturns by even more than

would be implied by recessionary reductions in bank capital alone. As loan securitization

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

stocks of real estate and consumer loans; this increase in asset illiquidity created “cross-sector

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loan overhang” effects, neutralizing equity capital that could otherwise have been used to back

new small business lending. As stock market declines made issuing new equity capital more

expensive, banks became more circumspect in their allocation of existing risk capital; this

increase in risk aversion exacerbated the overhang effects of existing portfolio loans, making

banks less likely to make the marginal business loan. Thus, our study provides a micro-theoretic

framework that helps explain recent empirical findings that small business lending declined in

Europe during the financial crisis (e.g., Popov and Udell 2010; Jimenez, Ogena, Peydro and

Saurina 2012; Cotugno, Monferra and Sampagnaro 2012). More to the point, we perform a

structural estimation of our theoretical loan supply function using lending data from U.S. banks,

and find parameter estimates that are strongly consistent with the predictions of our theory across

the business cycle.

The rest of the paper proceeds as follows. Section 2 provides a brief overview of the

bank lending literature most relevant to this study, first the theoretical then the empirical.

Section 3 presents our theory model of loan supply with capital market imperfections, which

links bank loan portfolio management to preexisting (i.e., overhanging) loan stocks, expected

loan profitability, current lending opportunities, loan performance covariances, and effective risk

aversion. Section 4 operationalizes the model for empirical estimation and lays out our main

hypotheses to be tested. Section 5 describes our detailed bank-level data set and defines the

variables used in our regression tests. Section 6 presents the results for our basic model of

business loan supply, some extensions of the basic model, and a simultaneous version of the

basic model that also includes loan supply functions for real estate loans and consumer loans.

Section 7 summarizes our main findings and discusses implications for policy.

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2. Related literature

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.3 Froot, Scharfstein and Stein (1993) show that firms facing costly

external finance, stochastic net worth, and 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 (1997)

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)

coined 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

3 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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cases, increases in risk overhang may lead firms to reduce their total exposure to the underlying

risk by canceling existing policies.

A large number of empirical studies on bank capital and lending investigate whether

implementation of the Basel I capital requirements caused a “credit crunch” in the U.S. In

general, these studies relate loan growth to capital measures and other controls.4 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

association between bank capital and loan growth. 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 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. Empirical studies by Black and Hazelwood

(2011), Duchin and Sosyura (2011) and Li (2011) all find at least some evidence of increased

lending (i.e., greater risk-taking) at banks that received government capital injections. The

4 Examples include Bernanke and Lown (1991), Hall (1993), Haubrich and Wachtel (1993), Berger and Udell (1994), Hancock and Wilcox (1993, 1994a, 1994b), Berger and Udell (1994), Brinkman and Horvitz (1995), and Peek and Rosengren (1995).

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findings of these studies are important; 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. Jimenez, Ogena, 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 small

and medium sized enterprise (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,

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.

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

studies focused on large banks, chiefly because regulatory capital constraints are more likely to

be binding for large banks and because large banks produce the lion’s share of the aggregate loan

supply. We focus on small banks because, for the reasons we outlined above, these banks

provide a more natural laboratory for testing the concepts developed in the theoretical corporate

finance literature on investment decisions when assets are illiquid and external capital is costly.

Second, previous studies estimated reduced-form regression models, whereas we estimate a

structural model that includes other loan supply decisions. This framework provides a more

complete test of risk-management practices at lending institutions and the effects of risk

overhang on loan supply. 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. Finally, within the small set of studies that have tested for small

business credit rationing during the financial crisis, we are one of the very few to take this

question to U.S. data.

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), Stein (1998), and 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

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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 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 (‘capital’), Lt-1,i in outstanding

loans in each sector i, and net external (‘debt’) finance of Ft-1=∑i (Lt-1,i) -Wt-1. Without loss of

generality, we assume that Ft-1 is positive, as is the case for most banks; we also 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+rt, 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+rt+pt-1,i-η~ t,i, where pt-1,i is the per dollar credit

5 We make this assumption for simplicity alone, as it is well known that issuing new equity also involves significant transaction and informational costs. While banks can issue long-maturity, federally insured retail deposits that are less likely to be affected by such information concerns, banks also regularly issue costly non-deposit debt instruments such as subordinated debt, trust preferred stock, and Federal Home Loan Bank advances. Moreover, insured deposits are not a perfect, costless substitute 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

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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+rt+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 that all losses on loans to

sector i 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

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. 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 (see Carey, 1998, and Winton, 2000). The assumption of normality allows us to give a simple, tractable analytic solution to the bank’s portfolio choice problem.

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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 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; and ][

][

W

WW

PE

PEG −= measures the

bank’s effective risk aversion (and we shall refer to its reciprocal 1/G as the bank’s risk

tolerance) induced by the costs of external finance.

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

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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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 we proceed to the data

and estimation, however, we must incorporate two features of the data that run counter to our

assumptions above. The first is that banks hold liquid as well as illiquid loan stocks. The second

is that we do not directly observe new loan supply, only the change in loan stock. We then

present our estimation equation and predicted outcomes for the regression parameters.

4.a. 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 with imperfect capital markets, it is optimal for banks to shed all

loans that can be sold at fair value. However, the market prices for loan sales may be below the

banks’ expected values due to information asymmetries or transaction costs of selling loans,

resulting in illiquid loans which are held rather than sold.

To include the effects of illiquid loan stocks, 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 (e.g., not rolled

over), 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')

15

While equation (3') is predicted by theory, the available data do not allow us to observe

the portions δt-1,i and δt-1,j of preexisting loan stocks that are illiquid. Instead, we must use the

total (liquid and illiquid) outstanding stocks of loans Lt-1,i and Lt-1,j in our estimation equations in

place of illiquid outstanding loans δt-1,iLt-1,i and δt-1,jLt-1,j. Thus, although equation (3') predicts

that the coefficient on outstanding same-sector loan stocks (δt-1,iLt-1,i) will be exactly -1, the

estimated coefficient in our regressions will reflect the effect of loan stock liquidity on the

supply of new same-sector loans.8

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

with exogenous conditions. A recession, or a downturn in a specific sector, will reduce the

liquidity of outstanding loans for two reasons. First, borrowers are in worse shape so they are

more likely to try to roll over their maturing loans. Second, the bank faces greater adverse

selection problems when trying to sell or securitize these increasingly risky loans. Additionally,

a recession or a sector downturn may have a capital effect: banks will expect increased future

losses on outstanding loans, which will reduce expected equity capital and make the bank

effectively more risk averse. We test for these effects by estimating our model separately during

(2007-2010) and prior to (1990-2006) the financial crisis.

4.b. New loans are unobservable

A second concern is that new loan supply NLS is not directly observable in the data.

Instead, we use the net period-to-period change in the stock of loans, which we refer to as the net

lending change, or NLC. Note that the stock of outstanding sector i loans Lt,i at the end of period

8 Given this substitution of Lt-1,i for δt-1,iLt-1,i in our estimations, a strict interpretation of the model (3') is that the estimated coefficient on Lt-1,i will reveal the average share of outstanding sector i loans that are illiquid. However, we make several additional adjustments to our estimation equation (e.g., we estimate the equation in loan shares rather than loan levels, to avoid size effects) which invalidate this strict prediction.

16

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))L t-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 net lending change 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, will hold some liquid loans for strategic purposes, and will hedge some of

these held liquid loans if the price of insurance is favorable. Regardless, banks will tend to draw

down or sell off a larger portion of their liquid outstanding loans when their capital falls (due to

increased risk aversion) or if the portfolio risk associated with their liquid loans increases (i.e.,

increased correlations with other loans). If the share of liquid loans (1–δi)Lt-1,i is small relative to

the flow of new loans or if the bank retains a large portion of its liquid loans—both conditions

are more characteristic of small banks than of large banks—then NLC will be highly correlated

with new loan supply NLS.

4.c. Specification

Equation (4) presents our estimation equation for business loan supply, which deviates

somewhat from the theoretical equation (3'). We use net lending change NLCt as a proxy for the

unobservable new loan supply NLtS; the Lt-1 measure total preexisting loans (not just the illiquid

portion δt-1Lt-1); the bank risk tolerance G-1 and risk-adjusted loan return (pt,i-µt,i)/σii measures are

specified separately (rather than multiplicatively) in order to estimate the independent effects of

17

these measures;9 the covariance-variance ratios σij/σii are suppressed; and the regression

coefficients φ, β, ρ, χ and ξ are parameters to be estimated:

11

11

1,1,1

3,2,11,11

3,2,1,

−

=−−−

=+

−+∑−∑−= t

tt

iitit

iitit G

pLLNLCNLC ξ

σµ

χρβφ (4)

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

consumer = 3) and t indexes time. The coefficients φ and ρ absorb the effects of the suppressed

covariance-variance ratios σij/σii while the coefficients β and ρ absorb the unobserved liquidity

effects δt-1 discussed above.

In our estimations, we additionally control for fixed bank effects, seasonal 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.d. 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

9 Estimating the model using the combined term yields only trivial differences in the other coefficients.

18

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.

• 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.

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

bank’s risk tolerance (ξ>0).

5. Data and Variables

We estimate equation (4) 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) from the first quarter of 1990 (1990:Q1) through the fourth quarter of 2010

(2010:Q4). We limit the data to include only so-called “community banks” with less than $2

19

billion in assets in real 2010 dollars.10 We exclude banks with less than $25 million in assets in

current dollars because the call reports contain very little detail for these tiny banks. We also

exclude banks located in rural areas, as rural banks face a different set of lending opportunities

than urban banks, which results in different exposures to loan overhang and different incentives

to deal with this risk.11

Since our goal is to examine banks’ loan portfolio decisions, we only consider banks that

make non-trivial amounts of loans in all three major categories of loans reported in the call

reports: business loans, real estate loans, and consumer loans. 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). These

upper and lower boundary restrictions eliminate around one-third of the bank-quarter

observations, and the restrictions become more binding over time. 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 decreasing during the financial crisis, while the asset share of business

loans remained relatively stable and the asset share of consumer loans declined by about half.12

Over time, as real estate loans provided a larger portion of small bank lending, and as consumer

10 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. 11 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. 12 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).

20

loan shares became less important at small banks, fewer banks qualified as “non-specialist”

lenders; hence, the number of observations in our tests unavoidably declines over time.

We make several additional data adjustments to avoid the effects of data errors, merging

banks, or banks with an abrupt change in lending strategy. 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. We also delete bank-quarter observations in which the assets of another bank are

acquired, bank-quarters when banks are less than 5 years old, all observations for banks that

never lend out more than 25% of their assets, and all observations for banks that were not present

in the data for at least five consecutive quarters.

This 1990-2010 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 self-reported small

business lending behavior of U.S. banks, as measured by the Federal Reserve’s Senior Loan

Officer Opinion Survey on Bank Lending Practices (SLOS). The SLOS 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 lending standards exceeded 10 percent for

21

the first time in the January 2008 SLOS, 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 SLOS, so we mark 2011:Q1 as the end of the crisis (i.e., 2010:Q4 is

the final quarter of the crisis).13 Hence, we refer to the 17 years of data from 1990:Q1 though

2007:Q3 as the “pre-crisis” period and the 16 quarters of data from 2007:Q4 through 2010:Q4 as

the “crisis” period.

5.1. The small bank lending environment

The limited lending capacity of small 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. 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). Because the supporting information for these ‘relationship loans’

cannot be credibly conveyed to outside investors, these loans should be less liquid than loans

based upon quantifiable information; Berger et al. (2005) find evidence consistent with this

prediction.

Real estate loans and consumer loans made by a given small bank may or may not be less

liquid than those made by larger banks. Large banks originate and securitize, or 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

13 In the January 2008 SLOS, 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 SLOS, 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.

22

receivables). The originate-and-securitize production process generates additional costs 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 the scale economies and

fee income associated with this process offset these costs for large lending operations. 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 lenders

may choose to securitize a smaller portion of the real estate and consumer loans they originate,

and hold a larger portion as portfolio investments. Moreover, because small banks have less

incentive to make loans that conform to the size, documentation, and credit score standards

necessary for securitization, the real estate and consumer loans made by small banks are more

likely to be idiosyncratic and hence less liquid. The principle exception to this is home mortgage

loans sold for securitization through government-sponsored enterprises such as Fannie Mae,

Freddie Mac and Ginnie Mae.

Small banks have several other attractive features for our study. Small banks operate

within a smaller geographic area than large banks and hence are less well diversified; this makes

small banks more sensitive to fluctuations in local business conditions that can shift their optimal

loan portfolio composition away from their current (perhaps illiquid) loan portfolio composition.

Small banks lack the scale and expertise to produce many nontraditional, off-balance-sheet

banking products (e.g., insurance and securities underwriting, securities brokerage, loan

securitization), so their strategic focus remains on traditional portfolio lending. This not only

makes small banks a relatively homogeneous population for statistical analysis, but also means

that lending portfolio concerns such as loan overhang should loom larger for small banks than

23

for large banks. During much of our period of investigation, small banks were less likely to be

involved in the kinds of mergers that significantly altered their business strategies. Because most

small banks lack the expertise to hedge credit and other risks with off-balance sheet derivative

securities, balance sheet-based measures are a more accurate measure of a small bank’s capacity

for bearing risk than they would be for a larger bank. And because a large portion of small U.S.

banks are family owned and managed, any lending decisions driven by risk aversion should be

relatively free of potentially confounding principal-agent effects.

5.2. Regression variables

The definitions of the variables used to specify the regression equations are presented in

Table 1, and descriptive statistics for these variables are displayed in Table 2, Panel A. We

define three categories of loans: business loans LBUS, real estate loans LRE, and consumer loans

LCON. Each of these three categories aggregates loans with different characteristics; while in

some cases this high level of aggregation is undesirable, this is unavoidable due to the structure

of the data in the call reports.14 LBUS includes all commercial and industrial loans. LRE includes

all loans 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. LCON 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.15 For all

14 While the call reports do disaggregate the portfolio balances for BUS, RE and CON loans into a variety of sub-categories, they do not disaggregate loan interest revenue. This precludes 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. 15 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.

24

three of these loan categories, we measure NLCit (the net lending change in sector i lending in

quarter t) as the end-of-quarter t loan stock minus the beginning-of-quarter t (end-of-quarter t-1)

loan stock, plus net loan charge-offs (loans charged off minus loans recovered) during the

quarter. In order to reduce the effect of size-induced differences between banks, we normalize

all loan stock and net lending change variables by dividing them by beginning-of-quarter t

assets.16

In our discussions above, we have characterized business loans as being less liquid, and

exhibiting greater credit risk, than consumer and real estate loans. The statistics displayed in

Table 2, Panel B provide confirmation. Credit risk data are displayed in item 1. Business loans

had the largest average quarterly loan charge-off ratio (0.62%), followed by consumer loans

(0.49%) and then real estate loans (0.09%). This ranking is unchanged when specialist lenders

are included in the averages. While 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. Business

loans are the least liquid, with increasing liquidity for consumer loans and the highest amount of

liquidity for real estate loans (which includes data on residential mortgages and home equity

loans, but not commercial real estate loans). Again, the ranking is unchanged when specialist

16 In the theory model we assume that loans are perfectly illiquid and once made never leave the balance sheet. Hence, NL is non-negative. In contrast, NLC (our empirical proxy for NL) is often negative because actual bank

25

lenders are included in the averages. 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.17

We measure the risk-adjusted return ratio (pt,1-µt,1)/σ11 for business loans with the

following ratio: the bank-specific expected returns on business loans in period t divided by the

market-specific variance of these returns over the entire sample 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 end of period t) multiplied

by the expected performance of business loans (the historical percentage of accruing business

loans) 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).18 The denominator in

this ratio is the variance of the quarterly change in expected profit from business loans for the

whole sample period, calculated separately for banks in each state.19

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

its total assets at the beginning of quarter t, denoted as EQt.20 Intuitively, banks with lower

loans are only imperfectly illiquid, and can leave the balance sheet via sales, maturity, or charge-offs. 17 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. 18 Historical nonaccruing loans are calculated as the four-quarter lagging average of nonperforming loans to beginning of period loan stock when available. When the four-quarter average is not available but a three-quarter average is, the three-quarter average is used. 19 While the theory model (3) does not constraint the loan performance variances and covariances to be constant over time, the quarterly call report data are simply too infrequent to construct good time-varying measures of these variables. We estimate the profit variance at the state level rather than at the bank level in order to ensure exogeneity. Using the variance of nonperforming loans instead of profit variance has no qualitative effect on the results. 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 1990-2010 sample period.

26

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.21

5.3. Loan performance covariances

In our theory model, the predicted direction of the cross-sector overhang and cross-sector

net lending effects depends on the whether the loan pairs in question co-vary positively or

negatively in performance. Table 3 displays the number and percentage of banks for which the

covariance of expected returns (pt - µt) was negative for each pair of loans, reported separately

for various sub-periods of our data sample.22 During normal times, increased business lending

provided the best opportunities for portfolio diversification gains: Cov(BUS,CON) was negative

for 56% of the banks and Cov(BUS,RE) was negative for 60% of the banks, although the data

were somewhat mixed during the three pre-crisis sub-periods. The largely negative values of

Cov(BUS,CON) and Cov(BUS,RE) during the pre-crisis period predicts positive signs for the

estimated cross-sector overhang and cross-sector net lending coefficients ρji and φji during those

years. During the crisis, business loans continued to co-vary negatively with consumer loans on

average (53%) but tended to co-vary positively with real estate loans (42%).

21 In our model, banks are only risk averse due to the costs of external finance, so banks with more equity to assets have greater ability to take on additional risky loans in the future. Thus, higher equity to assets indicates greater risk tolerance. By contrast, in models of managerial agency banks with more risk-averse managers will have higher equity to asset ratios, all else equal, since these managers hold more capital so as to reduce the bank’s risk of failure. In this alternative model, higher equity to assets would indicate higher (managerial) risk aversion. 22 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. 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) is calculated using historic, sector-wide loan quality data and does not rely on discretionary judgments by individual banks; hence, the covariances reported in Table 3 should be more accurate indicators of expected co-movements in loan performances.

27

In contrast, the expected returns on consumer loans and real estate loan tended to move in

concert with each other both before and during the financial crisis, which suggests fewer

opportunities for portfolio diversification among these two types of loans. (Note: These data will

provide useful predictions for cross-sector effects later in this study, when we estimate loan

supply functions for real estate and consumer loans.) The proliferation of positive return

covariances between RE and CON loans in our data likely reflects the manner in which these

loan categories are constructed in the call reports, where the category “real estate loans” includes

home equity lines of credit (HELOCs) and one-to-four family mortgages. Because loans backed

by residential real estate—and especially HELOCs—can serve as substitutes for consumer credit,

positive loan return covariances between real estate and consumer loans are not wholly

surprising.

6. Results

While business lending is the main focus of our study, the banks in our data make

simultaneous loan supply decisions for all three categories of loans in each quarter. Hence, in

equation (4), the right-hand-side variables NLCRE and NLCCON are simultaneously determined

with the dependent variable NLCBUS. We use a two-stage least squares (2SLS) approach to

address this endogeneity. As first-stage instruments, we add four measures of economic

conditions in bank i’s state that are likely to be correlated with changes in consumer and real

estate lending: the quarterly percent change in personal income, the quarterly percent change in

housing prices, the quarterly change in an index of coincident economic indicators, and the

quarterly unemployment rate. In addition to serving as good instruments, these state-level

variables serve as “demand shifters” and should help identify the underlying supply relationships

28

in our model.23 In the second stage, we include a vector of three quarter dummies to control for

seasonal lending effects and we also include selected state-level economic conditions (the

quarterly percent change in the number of employed workers and the quarterly percent change in

the number of unemployed persons) to control for demand-side macro-economic effects on

NLCBUS. Diagnostic tests (see Tables 4 and 5) indicate that our instruments are relevant and

valid. We estimate both stages using standard panel fixed effects techniques. Alternative

estimations in which we clustered standard errors at the bank level did not materially change our

results.

6.1. Business lending model

Table 4 displays the second-stage regression results for the business loan supply model

(4), which we estimated for various subsamples of time both before and during the financial

crisis. The results are substantially consistent with the predictions of our theory model, and

suggest that loan overhang/illiquidity contributed to a reduction in small business loan supply

during the financial crisis.

The coefficient on the same-sector overhang variable BUS is always negative and

statistically significant, as expected. The magnitude is non-trivial. For example, during the pre-

crisis period, a 10% increase in business loan overhang (BUS) is associated with a decline in

new business lending (NLC_BUS) in the following quarter equal to about 4/10ths of a percent of

the average bank’s business loan balance.24 Stated differently, this reduction in new business

23 All of the state-level economic conditions variables are seasonally adjusted; we regressed each time series on a vector of quarter dummies and then used the residuals from these regressions in our tests. Data on personal income growth are from the Bureau of Economic Analysis; data on employment growth, unemployment growth, and unemployment rates are from the Bureau of Labor Statistics; data on housing prices are from the Office of Federal Housing Enterprise Oversight; and the coincident economic indicators index is from the Federal Reserve Bank of Philadelphia. This set of variables has been used previously in research by Daly, Krainer and Lopez (2003) and Crone (2003). 24 Multiplying the same-sector loan overhang coefficient (-.0401) in column [1] by a ten percent increase in mean BUS (.10*.1198) and dividing by mean BUS (.1198) yields the result.

29

lending is equal to about 20% of the median bank’s quarterly increase in business lending during

the pre-crisis period (1.875%). But even this substantial quarterly effect understates the eventual

impact of loan overhang: the quarterly decline in new lending only partially draws down the

initial overhang in business loans, so similar reductions will accumulate over the quarters that

follow. If we assume that business loans are illiquid, have one-year maturities, and are

originated uniformly across time, then the cumulative reduction in NLC_BUS would be roughly

equal to 1.4% of the average bank’s loan balance.25 These effects triple in size during the

financial crisis: the coefficient on BUS increases in absolute magnitude from -0.0401 in column

[1] to -0.1488 in column [5]. This increase is consistent with a reduction in the liquidity of small

business loans during an economic downturn leading to more risk-averse portfolio management

and a tighter supply of small business credit.

In most cases, the coefficients on the cross-sector overhang variables RE and CON have

signs that are theoretically consistent with the loan performance covariances reported in Table 3.

For the pre-crisis period in column [1], we find the predicted positive cross-sector overhang

effect for both RE and CON, as predicted by the largely negative values for Cov(BUS,RE) and

Cov(BUS,CON) in the data. For the three pre-crisis sub-periods, we find the predicted signs on

RE and CON in five-out-of-six instances (only the positive sign on CON in column [3] is

inconsistent with theory). For the crisis period, the positive coefficient on CON is theoretically

consistent with the negative Cov(BUS,CON) for these years, while the coefficient on RE is

essentially zero (predicted negative). In all cases, the cross-sector overhang effects are smaller in

absolute magnitude than the corresponding same-sector overhang effects—that is, lenders expect

new business loan performance to co-vary more closely with their existing business loans than

25 The result is calculated as follows: -0.0401*(.10 + .075 + .05 + .025)*0.1198 = .0140 or 1.4%.

30

with their existing real estate or consumer loans. The impact of overhanging consumer loans

increased by an order of magnitude during the crisis—from 0.0109 in column [1] to 0.1314 in

column [5]—another indication that banks perceived loans to be less liquid during an economic

downturn. The lack of any similar real estate loan overhang effects during the crisis may reflect

the presence of the GSEs, which provided a ready source of liquidity for residential real estate

loans throughout the financial crisis.

Also consistent with our theory, the coefficients on the cross-sector net lending change

variables NLC_RE and NLC_CON closely match the signs and/or significance of their related

cross-sector loan overhang variables RE and CON. During the pre-crisis period, an additional

dollar of new consumer lending was associated with approximately $0.87 in additional business

lending; again, this overhang effect increased substantially during the crisis period, to

approximately $1.36.

As expected, the estimated coefficient on risk-adjusted loan return RAR is positive and

statistically significant throughout the pre-crisis period. This suggests that we are estimating a

loan supply relationship: when the risk-adjusted expected return from making business loans

increases, banks supply more net business loans. Prior to the crisis, a one standard deviation

increase in RAR is associated with increased business lending during the following quarter equal

to 4/10ths of a percent of the average bank’s business loan balance.26 The coefficient on the risk

tolerance variable EQ is also positive and statistically significant as expected during the pre-

crisis years. Increases in banks’ capital cushions—the most basic form of credit risk mitigation

at community banks—are associated with increases in business loan supply. Prior to the crisis, a

one standard deviation increase in EQ is associated with increased business lending during the

26 Multiplying the RAR_BUS coefficient (.0009) in column [1] by the standard deviation of RAR_BUS (.5093) and dividing by mean BUS (.1198) yields the result.

31

following quarter equal to 5/10ths of a percent of the average bank’s business loan balance.27

In contrast, neither RAR nor EQ has a statistically significant impact on business lending

during the crisis. The zero coefficient on RAR in column [5], strictly interpreted, indicates

perfectly inelastic business loan supply, which would be consistent with credit rationing (i.e.,

allocating credit based on non-price considerations) during uncertain economic times. However,

there is at least one other possible explanation for this result. The RAR coefficient in column [5]

is similar in magnitude to the significant RAR coefficient in column [1] but with a much higher

standard error; hence, the lack of statistical significance may simply reflect less precise

estimation due to a smaller subsample. We investigate this possibility in the next subsection.

The zero coefficient on EQ in column [5], interpreted within the strict confines of our theory

model, indicates that additions to capital did not bolster the average bank’s tolerance for risk

during the financial crisis. However, as discussed above, it has long been recognized that the

relationship between capital and risk-taking at banks may be non-monotonic: for poorly

capitalized banks in danger of insolvency, moral hazard incentives result in a negative capital-

risk relationship, while for healthy banks with no danger of insolvency (as in our theory model),

risk tolerance effects result in a positive capital-risk relationship. Hence, the zero coefficient on

EQ in column [5] may simply reflect these two offsetting effects in the data. We also investigate

this possibility in the next subsection.

Our estimates are strongly robust across the pre-crisis subsample periods reported in the

three columns in the center of Table 4. The signs, statistical significance, and economic

magnitudes of the coefficients are reasonably stable across these three subsamples, despite the

dramatic reduction in the number of observed banks from 2,936 to 1,078 during this time period.

27 Multiplying the risk tolerance coefficient (.0235) in column [1] by the standard deviation of EQ (.0251) and dividing by mean BUS (.1198) yields the result.

32

The only material differences are the coefficients on CON and NLC_CON, and these fluctuate as

predicted by the changes in Cov(BUS,CON) from Table 3. Hence, we find no obvious evidence

that changes in lending technologies during the sample period (e.g., credit scoring and loan

securitization) or changes in banking regulations during the sample period (e.g., FDICIA, Riegle-

Neal) materially affected business loan supply management at the small banks in our data.

6.2. Alternative specification for RAR and EQ effects

In Table 5, we test more formally whether the loan return (RAR) and risk-tolerance (EQ)

effects changed during the crisis period. We alter the regression specification by adding the

dummy variable CRS, which equals one during the crisis period and zero otherwise. We interact

this dummy with both RAR and EQ, and estimate the new specification using all of the data for

the entire 1990:Q1-2010:Q4 sample period. This approach should generate more precise

parameter estimates during the crisis period.

On average, the results in Table 5 largely confirm our earlier finding of a zero RAR

coefficient during the crisis. For the full sample regression in column [1], the derivative

∂NLC/∂RAR│CRS=1 is not significantly different from zero, consistent with perfectly inelastic

loan supply and credit rationing during the crisis period. In contrast, these new results contradict

our earlier finding of a zero EQ coefficient during the crisis. The derivative ∂NLC/∂EQ│CRS=1

is positive and statistically significant, and the coefficient on the interaction term EQ*CRS is

statistically zero; together, these two results indicate a positive link between bank capital and

business loan supply that was unaffected by the financial crisis. We will see below that this

result does not hold for all banks.

6.3. High versus low equity capital

In addition, we estimate the new specification separately for a subsample of low-capital

33

banks with EQ ≤ 8% and for a subsample of high-capital banks with EQ > 8%. If banks did

grow less risk tolerant (more risk averse) during the financial crisis, this set-up allows to test

whether this effect was monotonic across all banks or was limited to the high-capital banks that

have no hint of moral hazard incentives.

The strength of the loan overhang, loan supply, risk tolerance, and risk-adjusted return

effects varies materially with initial capital levels, as can be seen by comparing the coefficients

in the low-capital columns [2] and [3] to those in the high-capital columns [4] and [5]. The loan

overhang effects (BUS, CON, RE) and the cross-sector new lending effects (NLC_RE,

NLC_CON) are all larger in the low-capital subsample regressions. Similarly, business lending

by low-capital banks prior to the crisis was three times more sensitive to changes in EQ than was

business lending by high-capital banks (the EQ coefficients are 0.0640 and 0.0638 for low-

capital banks, but are only 0.0204 and 0.0202 for high-capital banks). These findings conform to

the spirit of our theory model, i.e., bank lending behavior becomes more risk averse as

investment capital becomes scarcer.

Banks’ reactions to capital shocks diverged during the financial crisis. At high-capital

banks, new business lending became more sensitive to changes in EQ during the crisis (a positive

coefficient on EQ*CRS). In the context of our theory, an extra dollar of capital had a more

powerful influence on the risk tolerance of these banks during the crisis, a time when capital was

relatively scarce and hence more expensive. This result is robust to whether capital was

increasing or decreasing at these banks: the triple interactive term EQ*CRS*DOWN (where

DOWN is a dummy equal to one in quarters after bank capital declines) never carries a

statistically significant coefficient. In contrast, business lending at low-capital banks lost all

sensitivity to changes in EQ during the crisis (the derivative ∂NLC/∂EQ│CRS=1 is statistically

34

zero for these banks). This result is consistent with a number of potential behaviors at low-

capital banks. First, any net new capital raised or otherwise injected during the crisis years was

absorbed rather than used to back expanded small business lending; this would be consistent with

pressure from bank supervisors to increase risk-weighted capital ratios. Second, any reduction in

equity capital suffered during the crisis years was not accompanied by reduced business lending;

this would be consistent with reallocating capital away from other loan sectors in order to

maintain valuable long-run business borrower relationships. Third, these banks simply became

less risk averse; in this case, the disappearance of the positive relationship between EQ and

NLC_BUS would be consistent with risk-seeking behavior at poorly capitalized banks (e.g.,

Merton 1977, Marcus 1984).

The risk-adjusted return effect is similarly affected by initial capital levels. Prior to the

crisis, the supply of new business loans was four times more sensitive to RAR at low-capital

banks than at high-capital banks. This stark difference in supply price sensitivity may indicate

that (during normal times) thinly capitalized banks attempt to grow earnings and replenish their

equity capital by aggressively pursuing high-yield lending opportunities. During the crisis years,

however, increases in expected loan returns did not generate additional loan supply for either set

of banks (the derivative ∂NLC/∂RAR│CRS=1 is never positive and significant during the crisis),

consistent once again with credit rationing during the financial crisis.

Finally, our specification provides a crude test of whether businesses that rely on

community banks for credit suffered from reduced loan supply during the financial crisis.

Differentiating Net Lending Change in Business Loans with respect to CRS indicates that

business loan supply at low-capital banks (∂NLC/∂CRS = -0.0037) declined during the crisis by

about twice as much as at high-capital banks (∂NLC/∂CRS = -0.0017), a sensible result that

35

conforms with the spirit of our theory. (Note that these tests are inclusive of other events that

occurred during the crisis period—for example, the regulatory responses to the crisis—that may

have materially added to or offset the primary small business loan supply actions of banks.)

6.4. Robustness tests

As described above, our sample selection technique eliminates “specialist” banks that

make and hold only a trivial amount of either business loans, real estate loans, or consumer

loans. Because we are estimating a model of banks’ loan portfolio decisions, this is an arguably

defensible procedure. However, there are two costs to this approach. First, this method of

sample selection could potentially result in biased coefficient estimates. Second, this method

greatly reduces the number of observations over time, as small banks abandoned consumer loans

and concentrated their portfolios in real estate loans (see Figure 1). In the first two columns of

Table 6, we re-estimate our basic models using a data set that includes both specialist and non-

specialist lenders. 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.

It is common in empirical banking studies to separate banks by asset size. While all of

the banks in our data are “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 this possibility, we re-estimate

our basic models for subsamples of quarterly observations for banks either above or below the

median value of assets each quarter. The results appear in the final four columns of Table 6. In

36

both the smaller bank and larger bank subsamples, the estimated coefficients nearly always carry

the same signs, statistical significance and orders of magnitude as in our earlier tests. The most

systematic difference is that the cross-sector and same-sector loan overhang and new lending

coefficients (the first rows of coefficients) tend to be larger for the smaller banks. This is a

sensible results: the risk-management deficiencies of these banks manifest themselves in more

risk-averse lending behavior, i.e., larger loan overhang effects.

Limitations in the structure of the call report data require us to aggregate different types

of real estate-backed loans—including residential mortgage loans, non-residential (commercial)

mortgage loans, and construction and development loans—in our RE variable. We cannot

construct the RAR variable for each of these types of loans, but we can observe the mix of these

loans within RE. We exploit this information to re-estimate our basic models for two

subsamples of banks. Banks have “commercial real estate focus” if their share of real estate

loans in commercial real estate (non-residential mortgage loans plus construction and

development loans) exceeds the quarterly sample medians; on average, these banks hold

relatively illiquid real estate loans. Banks have “residential real estate focus” if their share of

real estate loans in residential mortgages (1-to-4 family mortgages, multi-family mortgages, and

home equity loans) exceeds the quarterly sample medians; on average, these banks hold

relatively liquid real estate loans.28

The results are displayed in Table 7. There is little evidence that our inability to

disaggregate real estate lending has badly biased our earlier results. Nearly all of the estimated

coefficients carry the same signs and statistical significance as before. Moreover, the differences

28 Levitin and Wachter (2012) report that approximately 80 percent of commercial real estate credit is held in portfolio rather than securitized, while in recent years as much as 80 percent of residential mortgage credit has been securitized rather than held in portfolio. The authors also report that the commercial mortgage backed securities market “remained limited in size” prior to 2004, which includes the bulk of our 1990-2010 sample period.

37

in the liquidity of real estate holdings across the two subsamples generate results that are

consistent with the predictions of our theory. During the pre-crisis years, some of the

coefficients exhibit non-trivial differences in the magnitudes across the two subsamples. A

reduction in EQ dampened new business lending by about twice as much at the commercial real

estate-focused banks, consistent with greater risk aversion at banks with more illiquid portfolios

of loans. Similarly, a reduction in RAR had a much stronger negative impact on new business

lending at these banks.29 During the crisis years, both sets of banks continue to exhibit perfectly

inelastic business loan supply. Similar to our findings for low-capital banks, banks with

residential mortgage focus were insensitive to changes in EQ during the crisis; again, any net

new capital raised during the financial crisis at these banks did not reduce risk aversion by

enough to generate new business lending. Interestingly, the uniform reduction in business

lending during the crisis found above in Table 5 is found here only in the commercial real estate

focus subsample. Whether banks reduced credit supply in all sectors during the crisis, or simply

shifted from business lending to non-business lending, is taken up in the next section.

7. Portfolio loan supply model

To test more thoroughly test the predictions of our theory model, and to investigate

further the extent of loan overhang effects beyond those that impact business lending, we also

estimate a simultaneous version of our model that includes net lending change equations for all

three loan sectors. Formally, we estimate the following system of equations:

29 We also find substantial differences in magnitude in the cross-sector new lending estimates. The coefficients on NLC_RE are two-to-three times larger for the residential-focused banks, which is consistent with the RAR covariances in these data: the BUS-RE covariances were negative for 61% of the residential-focused banks compared to 57% of the commercial-focused banks. Similarly, the coefficients on NLC_CON are about two times larger for the commercial-focused banks, although we find only weak support for this result in the RAR covariances: the BUS-CON covariances were negative for 54% of the residential-focused banks compared to 55% of the commercial-focused banks.

38

11

11

1,1,1

3,2,11,11

3,2,1,

−

=−−−

=+

−+∑−∑−= t

tt

iitit

iitit G

pLLNLCNLC ξ

σµ

χρβφ

12

22

2,2,2

3,1,12,12

3,1,2,

−

=−−−

=+

−+∑−∑−= t

tt

iitit

iitit G

pLLNLCNLC ξ

σµ

χρβφ (4')

13

33

3,3,3

2,1,13,13

2,1,3,

−

=−−−

=+

−+∑−∑−= t

tt

iitit

iitit G

pLLNLCNLC ξ

σµ

χρβφ

where the subscript i =1,3 indexes real estate loans, business loans, and consumer loans,

respectively. The results—which we generate using data for the full sample period and

estimation techniques identical to those used above for the single-equation business loan supply

model—are displayed in Table 8.30 For convenience, the business loan supply regressions are

simply repeated from Table 5, column [1].

As predicted by our theory, the loan overhang effects increase with loan illiquidity. The

estimated same-sector overhang effect for business lending (-.0393) is twice as large as the

same-sector overhang effects for consumer loan supply (-.0182) and twice again as large as for

real estate loan supply (-.0097), consistent with the rank order of the loan liquidity averages in

Table 2, Panel B. All of the cross-sector coefficients are statistically significant with signs that

are consistent with the expected profit covariance data: the cross-sector loan overhang effects

between real estate and consumer loans are negative (-0.0122 in column [2], -0.0136 in column

[3]); the cross-sector new lending effects between real estate and consumer loans are negative as

well (-0.6805 in column [2], -1.1966 in column [3]); and all of the remaining cross-sector effects

are positive.

30 We estimate each of the three equations in (4′) separately using two-stage least squares. In each of the first stages, we control for endogeneity of the NLC terms, using as instruments a set of state-level economic conditions variables similar to those used in the single-equation business loan supply model (4). In each of the second stages, we include bank fixed effects, seasonal dummies, and selected state-level economic conditions variables as additional controls. (The coefficients on these additional control variables are not reported in Table 6). Further details are available from the authors upon request.

39

The perfect supply inelasticity that we observe during the crisis for business lending does

not extend to the other two lending sectors. The coefficient sum RAR + RAR*CRS carries the

expected positive sign for both real estate and consumer lending—thus, to the extent that banks

were rationing credit during the crisis, on average such behavior was limited to business lending.

But prior to the crisis, the RAR coefficient is statistically non-significant for both real estate and

consumer lending. There is no reason to expect perfect inelasticity/credit rationing during

normal times, so we need a different explanation for this result. Prior to the crisis, some banks

made real estate loans (e.g., home mortgages) and consumer loans (e.g., auto loans) with the

intent of securitizing them—in other words, the conditions in these two lending sectors prior to

the crisis were inconsistent with the assumption in our theory model that banks make illiquid

loans. If some of these loans were made with the intention of selling them, then the expected

positive supply relationship between loans added to the balance sheet (NCL_CON, NCL_RE)

and expected loan revenues (RAR, which for the marginal loan includes only loan origination

fees) is less likely to obtain. This explanation allows for the positive coefficients on RAR for

these loans during the crisis, when the breakdown in private loan securitization reduced the

liquidity of these loans.

The risk-tolerance effect is statistically significant in all three loan sectors, both prior to

and during the crisis—however, this effect is unexpectedly negative for real estate and consumer

lending. Hence, reduced risk tolerance during the crisis (proxied by reductions in EQ) appears to

have been manifested by movements out of small business loans—historically the riskier and

more illiquid investments—and into real estate and consumer installment loans. Note that this

result is not necessarily inconsistent with high rates of mortgage defaults during the crisis; the

result measures the consequences of a reduction in risk tolerance during the crisis, and as such

40

only requires banks to expect lower risk-adjusted returns on new small business loans than on

new real estate loans over the lifetimes of these loans. Holding risk tolerance (EQ) and expected

returns (RAR) constant, the onset of the crisis also resulting in a shift away from business loans

(i.e., ∂NLC_BUS/∂CRS = -0.0014) and toward real estate (i.e., ∂NLC_RE/∂CRS = 0.0016) and

consumer (i.e., ∂NLC_CON/∂CRS = 0.0019) loans. The latter two results may simply reflect

banks’ inability to securitize consumer and real estate loans during the crisis, resulting in

“involuntary warehousing” of these loans (see Table 2B above).

7. 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, reduced

new lending opportunities, and illiquid asset markets that make it more difficult to raise funds via

loan sales—take risk-averse actions to conserve equity capital. Such behavior by banks can

exacerbate economic downturns by restricting credit to small businesses which create a

disproportionate share of the new jobs in the U.S. economy. Following the theoretical work of

Froot and Stein (1998) and Gron and Winton (2001), we derive a model of bank portfolio

lending when external finance is costly. Our model predicts how banks’ small business lending

decisions are influenced by the composition of their preexisting (overhanging) loan portfolios,

their new lending decisions in other loan sectors, their equity capital balances, and the expected

returns to making new business loans. We test the predictions of our model using quarterly data

for small commercial banks in the U.S. between 1990 through 2010, paying special attention to

the years of the global financial crisis, which caused illiquidity in asset markets, substantial

declines in bank equity capital, and a massive economic downturn in the U.S.

41

Our empirical results indicate that during normal times, small banks manage their loan

portfolios in a manner generally consistent with our model. Over the seventeen years prior to the

financial crisis (1990-2006), the data indicate that banks allocated additional capital to business

loans when the expected returns to making these loans was high, when banks had plentiful

amounts of equity capital, when the expected returns from new business loans co-varied with

banks’ existing (overhanging) portfolio of loans and with bank’s non-business lending

opportunities. Moreover, all of these effects were stronger at thinly capitalized banks than at

well-capitalized banks. The data also indicate that small banks reallocated their portfolios

toward (illiquid) business loans, and away from (liquid) real estate and consumer loans, when

internal equity was more plentiful. These results are consistent with risk-averse portfolio

management in which current credit is allocated efficiently and scarce capital is conserved for

future profitable lending opportunities.

For the most part, these practices intensified during the financial crisis, which we define

here as the years 2007 through 2010. The impact of overhanging loans on new business lending

grew substantially stronger, as did the impact of internal equity capital, during the crisis. Both of

these findings imply that banks’ effective tolerance for risk declined during the downturn, when

overhanging loans become less liquid and external equity capital becomes more expensive. But

we also find evidence that suggests lending inefficiencies. Small business loan supply grew

highly inelastic during the downturn, consistent with credit rationing in the face of economic

uncertainty. And at thinly capitalized banks, new business lending did not decline with

reductions in equity capital during the crisis, a potential indication of risk-seeking behavior by

these banks.

Our results are consistent with the conclusions drawn in other (mostly European) studies

42

that bank behaviors have contributed to the reduction in small business lending during the

financial crisis. This indicates 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. Perhaps more importantly, we provide a micro-theoretic framework for explaining

those findings, and our empirical evidence identifies the channels through which the supply of

small business credit deteriorates during downturns: increased illiquidity in asset markets,

increased risk overhang in bank loan portfolios, and increased risk aversion by bank lenders.

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 do not make calculations cross-sector loan performance

covariances, but they likely attempt to approximate modern portfolio theory 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 co-vary

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

co-vary 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. In the end, we have to

give senior loan officers at stable and profitable community banks their props, if only for having

an effective internal model.

Our findings suggest that bank loan supply has pro-cyclical tendencies, and these

tendencies may exacerbate macro-economic cycles. As bank lending becomes more profitable

due to an economic or sector-specific expansion, banks’ equity capital, lending capacity, and

43

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 (or local geographic) 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.31 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 results suggest that equity

injections into already well-capitalized banks would have had a larger positive impact on small

business lending, because it would have increased these banks’ tolerance for taking risks during

a severe recession.

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

31 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.

44

behave differently. For example, large banks may be able to use alternative risk management

techniques to reduce overhang effects. 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.

45

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49

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50

Table 1: Variable Definitions

All variables except σii are bank-specific; we have omitted the bank subscript for simplicity. The phrase “end of period t-1” is identical to “beginning of period t.”

Variable name in the regressions

Variable name in equation (4)

Description of regression variable

NLC_BUS NLC_RE

NLC_CON NLCi,t

Net lending change: The change in sector i loan stock during period t (from the end of period t-1 through the end of period t), plus loan charge-offs and less loan recoveries during the period, normalized by bank assets at the beginning of the period.

BUS RE

CON L i,t-1

Outstanding loan stock: The loan stock in sector i at the end of period t-1, normalized by bank assets.

EQ Gt-1 Risk tolerance: Bank equity capital divided by bank assets at end of

period t-1.

RAR_BUS RAR_RE

RAR_CON (pi,t - µi,t)/σii

Risk-adjusted return: Expected return for loans in sector i in period t divided by the variance of expected returns in loan sector i divided by 100, where: Expected return is bank-specific interest revenue divided by loans in force (loan stock minus non-accruing loans) in sector i during period t-1, multiplied by the historical percentage of accruing loans in sector i (four 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 returns is the variance over the full sample period of the quarterly average of bank-specific expected returns in sector i in the state in which the bank main office is located.

NPL_BUS NPL_RE

NPL_CON NPLi,t

Sector downturn: An indicator variable equal to one if the nonperforming loans ratio for sector i, aggregated to the state-quarter-rural level, is in the highest quartile for the full data period in period t.

NPL_portfolio NPLPORTt Sector downturn effect on bank portfolio: A loan-share weighted average of the NPLi,t indicator variables in period t. The shares are the beginning of period loans to total assets for the three types of loans.

LIQ_high LIQ_low

LIQ t

Non-loan asset liquidity: Indicator variables equal to 1 if liquid assets (cash and securities) to total assets is in the top (bottom) quartile of the sample distribution for all banks at end of period t-1.

51

Table 2: Descriptive Statistics

Panel 2A: Selected statistics for panel of quarterly data on small U.S. commercial banks between 1990:Q1 and 2010:Q4. Unbalanced panel includes 77,855 quarterly observations from 3,568 separate banks. Definitions for all variables are displayed in Table 1.

mean median standard deviation

minimum maximum

Number of quarters per bank 38.2 36 20.4 5 88 Bank assets (millions of 2010 $) 198.3 105.4 252.3 18.1 1,975.2 NLC_BUS 0.0086 0.0065 0.0168 -0.0602 0.1549 NLC_RE 0.0024 0.0016 0.0115 -0.1448 0.1221 NLC_CON 0.0011 0.0004 0.0082 -0.1684 0.1868 BUS 0.1198 0.1043 0.0651 0.0154 0.5647 RE 0.3323 0.3296 0.1095 0.0278 0.7216 CON 0.1037 0.0855 0.0639 0.0160 0.7037 RAR_RE 3.5708 3.4639 2.1975 -4.2293 34.9670 RAR_BUS 0.4513 0.3321 0.5093 0.0022 23.0102 RAR_CON 1.5329 1.3368 1.1734 -1.3949 24.0313 EQ 0.0906 0.0851 0.0251 -0.0022 0.3709

Panel 2B: 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 1990-2010 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

All banks with less than $2 billion in assets

(includes specialist banks) 1. Loans charged-off, % of total loans (means of bank-quarter observations)

BUS 0.62% 0.96% RE 0.09% 0.15% CON 0.49% 0.61% 2. Loans sold or securitized for which banks have existing recourse exposure, % of total loans (means of quarterly aggregate ratios): BUS 0.06% 0.16% RE (excluding commercial real estate) 1.23% 2.88%

CON 0.98% 0.37%

52

Table 3: Expected Profit Covariances

Number and percentage of banks for which the expected profit covariances Cov(BUS,RE), Cov(BUS,CON) and Cov(RE,CON) were negative. ***, ** and * indicates a difference from 50% at the 1%, 5% and 10% levels of significance, respectively.

Sample Period: Precrisis Early Mid Late Crisis [90:Q1-07:Q3]

[90:Q1-95:Q4]

[96:Q1-01:Q4]

[02:Q1-07:Q3]

[07:Q4-10:Q4]

# banks 3,496 2,937 2,078 1,078 431

Cov(BUS,RE) # negative 2,111 1,879 1,055 590 197 % negative 60%*** 64%*** 51% 55%*** 42%**

Cov(BUS,CON) # negative 1,994 1,724 978 516 229

% negative 56%*** 59%*** 47%*** 48%*** 53*%

Cov(RE, CON)

# negative 1,510 1,302 779 420 166

% negative 43%*** 44%*** 38%*** 39%*** 38%***

53

Table 4: Two-stage least squares estimation of equation (4)

Selected results from two-stage least squares estimation of equation (4) for various time subsamples from the full 1990:Q1-2010:Q4 data set. All regressions also contain bank fixed effects, seasonal dummies, and time-varying state-level economic conditions variables (coefficient estimates not shown). NLC_RE and NLC_CON are instrumented using first stage regressions (not shown). ***, ** and * indicates statistical differences from zero at the 1%, 5% and 10% levels of significance, respectively. All variables are defined in Table 1.

[1] [2] [3] [4] [5] Dependent Variable: NLC_BUS

NLC_BUS NLC_BUS NLC_BUS

NLC_BUS

Sample Period:

Pre-Crisis [90:Q1-07:Q3]

Early [90:Q1-95:Q4]

Middle [96:Q1-01:Q4]

Late [02:Q1-07:Q3]

Crisis [07:Q4-10:Q4]

NLC_RE 0.3059*** 0.2344** 0.4736*** 0.1898** -0.1447

(0.0615) (0.0963) (0.1152) (0.0802) (0.5188)

NLC_CON 0.8713*** 0.6838*** 0.1809 -0.5154* 1.3575**

(0.1600) (0.1423) (0.1947) (0.2791) (0.6148)

BUS -0.0401*** -0.0992*** -0.0764*** -0.0833*** -0.1488*** (0.0022) (0.0036) (0.0048) (0.0053) (0.0201) RE 0.0084*** 0.0110* 0.0142*** 0.0108** 0.0010

(0.0013) (0.0059) (0.0048) (0.0053) (0.05309)

CON 0.0109*** 0.0397*** 0.0149*** -0.0284** 0.1314*

(0.0022) (0.0068) (0.0057) (0.0134) (0.0777)

RAR 0.0009** 0.0029*** 0.0012** 0.0028* 0.0010

(0.0003) (0.0004) (0.0005) (0.0016) (0.0070)

EQ 0.0235*** 0.0266** 0.0264*** 0.0422*** 0.0054

(0.0047) (0.0111) (0.0100) (0.0109) (0.0356)

Underidentification Test (p-value) 0.0000

0.0000 0.0000 0.0000

0.0818

Overidentification Test (p-value) 0.1133

0.2337 0.6200 0.1859

0.1663

Observations 74,256 35,575 26,303 12,142 3,485

Banks 3,495 2,936 2,077 1,078 432

54

Table 5: Two-stage least squares estimation of equation (4) with crisis interaction terms Selected results from two-stage least squares estimation of equation (4) for various subsamples of banks over the full 1990:Q1-2010:Q4 data period. All regressions also contain bank fixed effects, seasonal dummies, and time-varying state-level economic conditions variables (coefficient estimates not shown). NLC_RE and NLC_CON are instrumented using first stage regressions (not shown). ***, ** and * indicates statistical differences from zero at the 1%, 5% and 10% levels of significance, respectively. All variables are defined in Table 1.

[1] [2] [3] [4] [5]

Dependent Variable: NLC_BUS NLC_BUS NLC_BUS NLC_BUS NLC_BUS

Sample: All banks Low-capital banks

(EQ ≤8%) High-capital banks

(EQ>8%) NLC_RE 0.2817*** 0.3678*** 0.3665*** 0.2710*** 0.2699***

(0.0610) (0.0807) (0.0807) (0.0782) (0.0785)

NLC_CON 0.8906*** 0.8223*** 0.8249*** 0.6242*** 0.6248***

(0.1665) (0.2574) (0.2575) (0.1606) (0.1612)

BUS -0.0393*** -0.0544*** -0.0544*** -0.0438*** -0.0438***

(0.0021) (0.0035) (0.0035) (0.0027) (0.0027)

RE 0.0083*** 0.0144*** 0.0144*** 0.0059*** 0.0059***

(0.0012) (0.0023) (0.0023) (0.0013) (0.0013)

CON 0.0101*** 0.0151*** 0.0151*** 0.0099*** 0.0099***

(0.0020) (0.0039) (0.0039) (0.0025) (0.0025)

RAR 0.0008** 0.0023*** 0.0023*** 0.0006* 0.0006*

(0.0003) (0.0006) (0.0006) (0.0004) (0.0004)

RAR*CRS -0.0037* -0.0199*** -0.0205*** -0.0022 -0.0022

(0.0022) (0.0072) (0.0072) (0.0021) (0.0021)

EQ 0.0235*** 0.0640*** 0.0638*** 0.0204*** 0.0202***

(0.0045) (0.0199) (0.0199) (0.0053) (0.0053)

EQ*CRS 0.0061 -0.0947 -0.1039 0.0233** 0.0247**

(0.0094) (0.1398) (0.1400) (0.0096) (0.0097)

EQ*CRS*DOWN

-0.0268

-0.0039

(0.0184)

(0.0044)

CRS -0.0003 0.0121 0.0140 -0.0031** -0.0030**

(0.0011) (0.0106) (0.0107) (0.0012) (0.0012)

∂NLC/∂RAR│CRS=1 -0.0029 -0.0175** -0.0182** -0.0015 -0.0016

p-value 0.183 0.015 0.012 0.472 0.454

∂NLC/∂EQ│CRS=1 0.0296*** -0.0307 -0.0401 0.0437*** 0.0449***

p-value 0.002 0.825 0.773 0.000 0.000

∂NLC/∂EQ│CRS=1,DOWN=1 -0.0669 0.0409***

p-value 0.636 0.000

∂NLC/∂CRS -0.0014** -0.0037** -0.0016***

p-value 0.017 0.050 0.003

Underidentificaiton Test (p-value) 0.0000 0.0000 0.0000 0.0000 0.0000

Overidentification Test (p-value) 0.2040 0.1849 0.1822 0.1466 0.1383

Observations 77,779 29,379 29,379 48,073 48,073

Banks 3,515 2,407 2,407 2,667 2,667

55

Table 6: Robustness tests: Specialist banks and bank size subsamples

Selected results from two-stage least squares estimation of equation (4) for various subsamples. Specialist banks (columns [1] and [2]) hold relatively small amounts of either BUS, RE and/or CON loans. The median assets threshold (columns [3] through [6]) is calculated separately in each quarter of the data. All regressions also contain bank fixed effects, seasonal dummies, and time-varying state-level economic conditions variables (coefficient estimates not shown). NLC_RE and NLC_CON are instrumented using first stage regressions (not shown). ***, ** and * indicates statistical differences from zero at the 1%, 5% and 10% levels of significance, respectively. All variables are defined in Table 1.

[1] [2] [3] [4] [5] [6]

Dependent variable: NLC_BUS NLC_BUS NLC_BUS NLC_BUS NLC_BUS NLC_BUS

Sample: Non-specialist banks and

specialist banks Banks with above-median

assets Banks with below- median

assets

Pre-Crisis Full Sample Pre-Crisis Full Sample Pre-Crisis Full Sample

NLC_RE 0.3315*** 0.0695** 0.4934*** 0.2602*** 0.3123*** 0.1268

-0.0629 (0.0312) (0.1435) (0.0932) (0.0680) (0.1125)

NLC_CON 0.9285*** 2.1589*** 0.7486* 1.2439*** 0.5807*** 1.0441***

(0.1905) (0.2325) (0.4068) (0.2554) (0.1363) (0.2638)

BUS -0.0219*** -0.0154*** -0.0480*** -0.0433*** -0.0474*** -0.0429***

(0.0016) (0.0015) (0.0036) (0.0032) (0.0030) (0.0036)

RE -0.0005 0.0043*** 0.0097*** 0.0126*** 0.0077*** 0.0069***

(0.0011) (0.0010) (0.0031) (0.0023) (0.0015) (0.0015)

CON 0.0092*** 0.0122*** 0.0064* 0.0089*** 0.0138*** 0.0194***

(0.0016) (0.0016) (0.0035) (0.0028) (0.0033) (0.0046)

RAR 0.0017*** 0.0005 0.0017*** 0.0010** 0.0010*** 0.0003

(0.0003) (0.0003) (0.0006) (0.0005) (0.0004) (0.0006)

RAR*CRS -0.0011 -0.0050 -0.0024

(0.0009) (0.0037) (0.0030)

EQ 0.0127*** 0.0079** 0.0244*** 0.0310*** 0.0207*** 0.0209***

(0.0029) (0.0031) (0.0079) (0.0074) (0.0067) (0.0067)

EQ*CRS 0.0038 0.0076 0.0168

(0.0054) (0.0167) (0.0130)

CRS -0.0013* 0.0001 -0.0017

(0.0007) (0.0019) (0.0016)

∂NLC/∂RAR│CRS=1 -0.0006 -0.0040 -0.0021

p-value -0.0010 -0.0037 -0.0030

∂NLC/∂EQ│CRS=1 0.0118** 0.0386** 0.0377***

p-value -0.0053 -0.0179 -0.0134

∂NLC/∂CRS -0.0011*** -0.0013 -0.0014

p-value 0.000 0.138 0.130

Observations 145,032 166,976 37,040 38,796 37,108 38,873

Banks 5,273 5,418 2,037 2,068 1,996 2,006

56

Table 7: Robustness tests: Real estate lending subsamples Selected results from two-stage least squares estimation of equation (4) for various subsamples. We define commercial real estate loans as the sum of construction and development loans and non-farm, non-residential mortgage loans. The commercial real estate focus subsamples contain all quarterly observations in which the ratio of commercial real estate loans-to-total real estate loans exceeds the annual median. Similarly, the residential mortgage focus subsamples contain all quarterly observations in which the ratio of commercial real estate loans-to-total real estate loans is less than the annual median. All regressions also contain bank fixed effects, seasonal dummies, and time-varying state-level economic conditions variables (coefficient estimates not shown). NLC_RE and NLC_CON are instrumented using first stage regressions (not shown). ***, ** and * indicates statistical differences from zero at the 1%, 5% and 10% levels of significance, respectively. All variables are defined in Table 1.

[1] [2] [3] [4]

Dependent Variable: NLC_BUS NLC_BUS NLC_BUS NLC_BUS

Sample: Commercial real estate focus Residential mortgage focus

Pre-crisis Full sample Pre-crisis Full sample

NLC_RE 0.17838** 0.11034 0.33219*** 0.35274***

(0.07459) (0.08102) (0.08891) (0.08466)

NLC_CON 1.21939*** 1.36626*** 0.73428*** 0.72689***

(0.24105) (0.27416) (0.17957) (0.18115)

BUS -0.04665*** -0.04662*** -0.04783*** -0.04639***

(0.00333) (0.00330) (0.00326) (0.00321)

RE 0.01174*** 0.01278*** 0.01229*** 0.01175***

(0.00232) (0.00243) (0.00158) (0.00152)

CON 0.01418*** 0.01476*** 0.01273*** 0.01116***

(0.00296) (0.00294) (0.00431) (0.00404)

RAR 0.00150*** 0.00108* 0.00066* 0.00067*

(0.00058) (0.00061) (0.00036) (0.00035)

RAR*CRS -0.00246 -0.00184

(0.00405) (0.00280)

EQ 0.03457*** 0.03823*** 0.01793*** 0.01713***

(0.00773) (0.00784) (0.00671) (0.00638)

EQ*CRS 0.01324 0.00114

(0.02111) (0.01108)

CRS -0.00212 0.00029

(0.00226) (0.00141)

∂NLC/∂RAR│CRS=1 -0.0014 -0.0012

p-value 0.732 0.678

∂NLC/∂EQ│CRS=1 0.05147** 0.0183

p-value 0.016 0.118

∂NLC/∂CRS -0.0020** -0.0005

p-value 0.044 0.563

Observations 37,035 38,793 36,965 38,727

Banks 2,340 2,384 2,151 2,165

57

Table 8: Two-stage least squares estimation of the three-loan system of equations (4′)

Selected results from two-stage least squares estimation of the system of equations (4′) for the full 1990:Q1-2010:Q4 data period. All regressions also contain bank fixed effects, seasonal dummies, and time-varying state-level economic conditions variables (coefficient estimates not shown). Right-hand side variables NLC_RE, NLC_BUS and NLC_CON are instrumented using first stage regressions (not shown). ***, ** and * indicates statistical differences from zero at the 1%, 5% and 10% levels of significance, respectively. All variables are defined in Table 1.

[1] [2] [3]

Dependent Variable: NLC_BUS NLC_RE NLC_CON

Sample Period: Full sample (1990:Q1 - 2010:Q4)

NLC_BUS 1.8724*** 2.7632*** (0.1341) (0.8387) NLC_RE 0.2817*** -1.1966*** (0.0610) (0.2373) NLC_CON 0.8906*** -0.6805***

(0.1665) (0.1383)

BUS -0.0393*** 0.0902*** 0.1246*** (0.0021) (0.0057) (0.0354) RE 0.0083*** -0.0097*** -0.0136***

(0.0012) (0.0021) (0.0029) CON 0.0101*** -0.0122*** -0.0182***

(0.0020) (0.0035) (0.0063) RAR 0.0008** -0.0000 0.0004

(0.0003) (0.0001) (0.0003)

RAR*CRS -0.0037* 0.0007* 0.0015* (0.0022) (0.0004) (0.0009) EQ 0.0235*** -0.0368*** -0.0543*** (0.0045) (0.0095) (0.0205) EQ*CRS 0.0061 -0.0062 -0.0160 (0.0094) (0.0185) (0.0269) CRS -0.0472*** 0.0605*** 0.0017 (0.0121) (0.0129) (0.0166) ∂NLC/∂RAR│CRS=1 -0.0029 0.0007* 0.0019*

p-value 0.183 0.099 0.051

∂NLC/∂EQ│CRS=1 0.0296*** -0.0430** -0.0704*

p-value 0.002 0.029 0.053

∂NLC/∂CRS -0.0014** 0.0016** 0.0019*

p-value 0.017 0.020 0.074 Observations 77,779 77,779 77,779 Banks 3,515 3,515 3,515

58

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)