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Federal Reserve Bank of Chicago

Risk Overhang and
Loan Portfolio Decisions
Robert DeYoung, Anne Gron and
Andrew Winton

WP 2005-04

Risk Overhang and Loan Portfolio Decisions
Robert DeYoung*
Federal Reserve Bank of Chicago
Anne Gron**
Northwestern University
Andrew Winton
University of Minnesota

August 2005

Abstract: Despite operating under substantial regulatory constraints, we find that commercial
banks manage their investments largely consistent with the predictions of portfolio choice
models with capital market imperfections. Based on 1990-2002 data for small (assets less than
$1 billion) U.S. commercial banks, net new lending to the business, real estate, and consumer
sectors increased with expected sector profitability, tended to decrease with the illiquidity of
existing (overhanging) loan stocks, and was responsive to correlations in cross-sector returns.
Small banks are most appropriate for this study, because they make illiquid loans and manage
risk via on-balance sheet (non-hedged) diversification strategies.
JEL codes: G11, G21
Key words: commercial banks, loans, portfolio choice, risk overhang
An earlier version of this paper had the title “Risk Overhang in the Banking Industry.” We thank
Allen Berger, Robert Bliss, Mark Carey, Doug Evanoff, Evren Ors, Mitchell Petersen, Greg
Udell, and seminar participants at the FDIC, the Federal Reserve Bank of Chicago, 2004
Conference on Bank Structure and Competition, and the 2005 International Industrial
Organization Conference. Nick Kreisle and Jianjun Wu for research assistance. All errors are
our own.
* The views expressed in this paper do not necessarily reflect those of the Federal Reserve Bank
of Chicago or the Federal Reserve System.
** Corresponding author: Anne Gron, Kellogg School of Management, Northwestern
University, Evanston, IL 60208-2001, agron@kellogg.northwestern.edu.

Introduction
Commercial banks play a central role in the supply of credit. About one-third of all
household debt is obtained from commercial banks, and about two-fifths of all small businesses
obtain some form of credit from a commercial bank.1 Recent theory suggests that, when external
finance is costly, value-maximizing banks make asset allocation and capital budgeting decisions in a
risk-averse manner: they base new lending decisions not only on expected loan returns, but also on
their available capital and on the covariance of these returns with their existing loan portfolio. Such
behavior increases a bank’s expected profit by reducing the probability that the bank finds itself with
too little internal capital to fund a valuable loan in the future. This theorized behavior also affects
borrowers, particularly small business borrowers who rely primarily on commercial bank lending for
financing: in the long run, their bank is more likely to be around to finance them, but in the short run,
they may face credit rationing during periods of high effective bank risk aversion.
In this paper, we investigate whether small commercial banks’ lend in a manner consistent
with this risk management and capital budgeting paradigm. As just noted, commercial banks provide
vital access to capital and credit for small businesses and consumers, and this is especially true of
small, locally focused commercial banks—even though these so-called “community banks” represent
a relatively small share of total credit supply, they are a critical source of funding for informationally
opaque small businesses and as such are important for economic growth.2 We focus on the effect of
‘risk overhang,’ the risk represented by illiquid, outstanding loan stocks on net new lending. 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.3 The degree of information asymmetry and
liquidity varies across types of banks, types of loans, and types of borrowers. For example, as there is
typically more publicly-available information on large firms and large firms are more likely to have
publicly-traded shares and debt, the bulk of business loan sales involve loans to large businesses
rather than small businesses. Risk overhang is likely to be a greater concern for small banks, since
their business borrowers are typically small, privately-held firms and their consumer loan portfolios
1

Based, respectively, 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).
2
As described in Petersen and Rajan (1994), Berger, Saunders, Scalise, and Udell (1997), Berger et al. (2005), and
elsewhere, small banks engage in more relationship lending that small businesses utilize. More recently, however,
Petersen and Rajan (2002) and Berger, Rosen, and Udell (2001) find that over time larger banks are providing more
small business loans. Berger, Hasan, and Klapper (2004) document a positive empirical link between a large,
healthy small banking sector and macroeconomic growth across 49 developed and developing nations.
3
Seminal papers on delegated monitoring include Diamond (1984), Ramakrishnan and Thakor (1984), Boyd and
Prescott (1986), and Williamson (1986).

1

are often too small to permit cost effective securitization. Small banks have little or no access to
public funding markets, increasing their costs of external financing and thus increasing their need to
manage asset risk effectively. These banks are also less likely to use credit derivatives such as credit
swaps, so they must manage the risk of their loan portfolios through on-balance sheet loan
concentrations. Thus, we test for the effects of risk overhang at small U.S. commercial banks with
assets less than $1 billion—banks for which loan portfolio effects can be more accurately measured
and are more relevant as a measure of bank risk-management activity. We note that our definition of
‘small bank’ includes well over 90 percent of all commercial banks in the U.S.
Using the capital budgeting model of Froot and Stein (1998), we begin by deriving a model
of bank loan supply that explicitly illustrates the effect of risk. Our model generates empirically
tractable predictions about the effects of risk overhang, expected loan returns, and competing lending
opportunities on banks’ supply of new loans, given their current portfolio composition and capital.
We test these loan supply predictions for small commercial banks located in urban and rural markets
between 1990 and 2002, measuring new loan supply as the net quarterly change in the portfolio
shares of three different types of loans—real estate loans, business loans (which includes agricultural
production loans for banks in rural markets), and consumer loans. We use two-stage least squares to
control for the simultaneity of net lending decisions across these different sectors.
Overall, we find that small banks make capital allocation decisions that are consistent with
risk-averse value-maximizing behavior. For example, controlling for expected returns, we find that
banks make fewer net new loans when the riskiness of current lending opportunities is positively
correlated with the riskiness of their existing stocks of loans. This risk overhang effect is larger when
the existing loan stocks are less liquid and when the risk correlation is greater. These effects are
particularly clear when we examine the impact of outstanding loan stocks on net lending within the
same sector—the negative impact of outstanding stocks of business loans on net business lending is
significantly greater than the same-sector overhang effect in the typically more liquid and less risky
real estate (mostly home mortgages) or consumer loan sectors. In general, these risk overhang effects
are exacerbated by temporary reductions in the liquidity of outstanding loan stocks caused by
downturns in local economic markets and/or individual loan sectors.
We find evidence that technological advance, government policy, and the nature of bankborrower relationships may have significant influences on the size and existence of risk overhang at
small banks. Our measured loan overhang effects tend to be weaker in the second half of the sample,
consistent with increased loan liquidity due to improved financial processes and information
technologies (e.g., credit scoring, asset securitization, deeper secondary markets for loans). The

2

exacerbating effects of economic downturns on loan overhang are more moderate in the business
loan sector, perhaps because small banks have incentives to preserve valuable relationships with their
small business clientele across the business cycle. This moderation is especially strong for business
lending at rural banks, likely because a portion of the realized credit risk of farm loans at these banks
is absorbed by government loan guarantees during agricultural sector downturns. Evidence of local
focus is especially strong in our data: even for multi-bank organizations where there may exist the
potential for inter-bank diversification, our findings suggest that portfolio management occurs at the
bank level.
Our estimates confirm that we are estimating a supply relationship. Net lending increases
when expected return is greater, but the effect of expected return is reduced somewhat if the loans are
expected to be less liquid or more risky due to current conditions. We also find some evidence that
banks with lower capital behave in a more risk averse fashion, especially for the riskiest loan sector
(business loans) and during the riskiest period of our sample; however, this relationship is less clear
for other sectors.
Our findings also support loan-supply motivations for the pro-cyclic nature of bank lending.4
During an economic expansion demand for lending is high and business profitability is good,
resulting in more profitable loans, more bank capital, and an expanding credit environment in which
banks lend more at lower rates as they compete for business. As the economy slows, some businesses
will suffer lower income or even losses, leading to delinquent loan payments or outright default,
reductions in bank capital, and a tighter credit environment as banks make fewer loans at higher
rates.5 Our findings indicate that risk overhang effects from outstanding loans work to decrease loan
supply during a recession even more than would be implied by the reduction in bank capital alone.
Outstanding loan stocks may become less liquid: banks face greater adverse selection problems when
trying to sell or securitize a riskier loan portfolio, and these are compounded by the fact that
borrowers in weaker financial positions are more likely to try to roll over existing loans rather than
repay them. Because economic shocks are generally correlated across economic agents, capital
contractions or expansions will affect a significant portion of banks simultaneously, resulting in
market-wide contraction or expansion of loan supply.

4

Although our explanation focuses on bank capital, loan illiquidity, and risk aversion, there are other models of
loan-supply procyclicality. Rajan (1994) presents a models credit cycles based on agency problems within banks.
Berger and Udell (2003) present a behavioral model. Ruckes (2004) models changes in bank credit standards as a
function of cyclical changes in loan quality and adverse selection problems.
5
This example is done in terms of business loans, but a similar story can be told for consumer and real estate
lending.

3

The rest of the paper proceeds as follows. Section 2 provides a brief overview of the bank
lending literature, first the theoretical then the empirical. Section 3 presents our theoretical model of
loan supply with capital market imperfections, which links bank loan portfolio management to
existing (i.e., overhanging) loan stocks, expected loan profitability, current lending opportunities,
loan covariances, and effective risk aversion. Section 4 operationalizes the model for empirical
estimation and lays out our main hypotheses to be tested. Section 5 presents our detailed bank-level
data set and regression variables. Section 6 analyzes our empirical results. Section 7 summarizes our
main findings and discusses implications for policy.

2. Related literature
Our work is most closely related to theoretical work examining how financial institutions
should manage their portfolios when they face costs of external financing linked 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.6 Froot, Scharfstein and Stein (1993) show that firms facing
costly external finance, stochastic net worth, and attractive future investment opportunities behave in
a risk averse manner. Froot and Stein (1998) extend this to a model of financial institutions in which
institutions’ new investments are influenced not only by capital structure, but also by their existing
asset portfolios and their ability to hedge new and existing risk. Froot and Stein 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 nontradable) asset exposures, and the covariance of the non-tradable cash flows of any other new
investments the firm is considering.
Froot and O’Connell (1997) and Gron and Winton (2001) provide specific applications of
this framework. Froot and O’Connell 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 focus on how outstanding risk exposures affect the current supply of firms’ risky
products, such as insurance policies or loans. They refer to these outstanding, illiquid exposures as
‘risk overhang’ and show that changes in risk overhang, such as a change in the distribution of the
6

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 Thakor (1996), Holmstrom and Tirole (1997), Besanko and Kanatas (1996) and Diamond and Rajan
(2000).

4

cash flows or a change in the covariance of past exposures with current opportunities, may
significantly reduce current supply. In extreme cases, increases in risk overhang may lead firms to
reduce their total exposure to the underlying risk by canceling policies they have written, calling
outstanding loans they have made, and so forth.
Much of the empirical literature on bank capital and lending stems from the debate over
whether implementation of the 1988 Basle Accord’s capital requirements caused a “credit crunch” in
the U.S. In general, these studies relate overall or sectoral loan growth to capital measures and other
controls.7 While this literature yields no consensus on the relationship between capital and loan
supply, Sharpe (1995) identifies two robust results across 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 evidence suggesting
that banks with higher capital growth relative to assets have greater increases in their loan portfolios,
with the most significant effects coming from the most capital-constrained banks.8
The empirical research on loan supply most closely related to our work is Hancock and
Wilcox (1993, 1994a, 1994b) and Berger and Udell (1994). These papers focus on how capital levels,
changes in capital requirements, and shocks to capital affect the supply of loans. Similar to the
literature cited above, no clear consensus about the relation between bank capital and loan supply
arises from this literature, although it does appear that negative capital shocks such as increases in
nonperforming loans reduce loan supply.
Our paper differs from the previous literature in several respects. First, 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. In
contrast, we focus on small banks and the role of risk overhang for the reasons outlined above: small
banks are more likely to be affected by risk overhang because their loans tend to be illiquid; small
banks are more likely to suffer from risk aversion induced by costs of external financing because
they do not have access to public funding markets; and small banks are more likely to manage credit
risk on-balance sheet because they are typically unable to use credit derivatives. Second, previous
studies estimated reduced-form regression models, whereas we estimate a structural model that

7

Examples of this literature include Bernanke and Lown (1991), Hall (1993), Berger and Udell (1994), Haubrich
and Wachtel (1993), Hancock and Wilcox (1994), Brinkman and Horvitz (1995), and Peek and Rosengren (1995).
8
More specifically, Gron and Beatty find that banks with higher increases in equity relative to assets have greater
growth in risk weighted assets.

5

includes other loan supply decisions. This framework provides a more complete test of riskmanagement 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 a 12-year period.

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.9 In addition to current period loans, the bank may
be able to make profitable loans in future periods. As shown by Froot, Scharfstein and Stein (1993),
profitable future investment opportunities combined with costly external funds and stochastic internal
funds cause the firm's objective function to be increasing and generally concave in the stock of
internal funds. Intuitively, more internal funds lessen the extent to which a bank 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-1i in outstanding loans
to sector i, and net external (debt) finance of Ft-1=∑i (Lt-1i) -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.10 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-1i loans to sector i regardless of its subsequent decisions in period t, Lt-1i is the bank’s
risk overhang in sector i in period t.
During period t the bank can make new loans, NLti ≥ 0, to each sector i, resulting in end of
period outstanding debt of Ft = ∑i (Lt-1i+ NLt,i) - Wt-1. The gross per dollar cost of debt funding is
9

Although the cost of federally insured retail deposits is less likely to be affected by such information concerns,
insured deposits are not a perfect, costless substitute for uninsured deposits. Billett et al. (1998) find that large banks
with rated public debt that is downgraded do increase their use of insured deposits after the downgrade, but this
increase is more than offset by their decreased use of uninsured liabilities.
10
We assume that external finance takes the form of debt for simplicity alone; it is well known that issuing equity
also involves significant transaction and informational costs.

6

1+rt, which includes any costs of accessing external markets rather than using internal capital.11
~
During period t, the bank realizes the gross per dollar return of Rti / t −1 on loans to sector i that were

~
originated in period t-1. Rti / t −1 equals 1+rt+pt-1i- η~ ti, where pt-1,i is the per dollar credit spread or
markup charged on sector i loans that originated in period t-1, and η~ ti is the random per dollar loan
~
losses on sector i loans in period t. Similarly, the bank realizes the gross per dollar return Rti / t =

1+rt+pti- η~ ti on the new loans to sector i originated in period t, where pti 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: η~ti ~ N ( µ ti , σ ti ) where both µti and σti depend on the sector’s economic
outlook at the start of that period.12 Both µti and σti 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
n
~
~
~
Wt = ∑ [ Lt −1i Rti / t −1 +NLti Rti / t ] − Ft (1 + rt )
i =1

n

= W0 (1 + rt ) + ∑ [ Lt −1i ( pt −1i
i =1

− η~ti ) +NLti ( pti − η~ti )]

(1)

~
~
where we have made use of the definitions of Rti / t −1 , Rti / t , and Ft.

~
The bank chooses new loan amounts, NLti, that maximize expected profit, E[P( Wt )] given
the financing constraints. This leads to the following first order condition for each sector i:
~
∂Wt
0 = E[ PW
] = E[ PW ( pti − η~ti )] = E[ PW ]( pti − µti ) − Cov( PW ,η~ti )
∂NLti

(2)

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

~

and the level of internal funds, Wt , are both normally distributed, we can apply Stein’s Lemma and
the definition of covariance to derive the bank’s supply of new loans to sector i, NLSti :13
11

Once more, we assume that Ft is positive. We could easily incorporate net negative debt as holdings of marketable
securities yielding 1+rt-ct, where ct is the additional cost (i.e., transaction costs plus any costs of asymmetric
information) of external finance over and above the return to investors holding marketable securities.
12
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.
~
~
13
Stein’s lemma implies that Cov(PW, η~ti ) = E[PWW]Cov( Wt , η~ti ). We also use Cov( Wt , η~ti ) = − ∑ j (Lt −1 j + NLtj )σ ij .

7

NLSti = −∑ j ≠ i NLStj

In (3), G = −

σ ij
σ ii

− Lt −1i − ∑ j ≠i Lt −1 j

σ ij
σ ii

+

p ti − µ ti
.
Gσ ii

(3)

E[ PWW ]
measures the bank’s effective risk aversion induced by the costs of external
E[ PW ]

finance, and we have suppressed the time subscript on the covariance and variance terms.
The bank’s supply of new loans is determined by several factors—the bank’s existing
exposures to risks, the correlations between the new loans and existing exposures, the bank’s other
new loan opportunities in sectors j≠i, and the attractiveness of the new loans normalized by the
bank’s risk tolerance. The first term on the right hand side of equation (3) accounts for the risk
impact of alternative lending opportunities on lending to sector i, and equals the net effect of new
lending opportunities in other sectors j and the covariance-variance ratios σij/σii (which we measure
as the covariance of loan losses in sectors i and j to the variance of loan losses in sector i). The
second term is the existing portfolio exposure in sector i, that is, the overhang of outstanding loans in
sector i at time t. The third term is the combined effect of the risk overhang in each of the other
sectors j and their covariance-variance ratios. The last term represents the attractiveness of sector i
loans to the bank: the return–risk (or Sharpe) ratio (pti-µti)/σti multiplied by the bank’s tolerance for
risk G-1 (the inverse of the bank’s risk aversion G).
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’) pti and decreasing in
expected loan losses (or costs) µit. Assuming that pti exceeds µti, 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-1i. Finally, if the covariance between sector i and
sector j is positive, then the supply of new loans in sector i is decreasing in both the overhang of
outstanding loans in sector j and the supply of new loans in sector j; by contrast, if the covariance is
negative, then the supply of new loans in sector i is increasing in loans to sector j.

4. Loan Supply with Capital Market Imperfections: Issues for Empirical Specification
Equation (3) forms the basis for our empirical analysis. Before 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.

8

4a. 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-1i ∈ (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 either run off naturally or else can be sold off at no cost to make room for new
loans. Since only illiquid loan stocks will affect new lending, we can rewrite equation (3) as follows

NLSti = −∑ j ≠i NLStj

σ ij
σ ij pti − µ ti
− δ t −1i Lt −1i − ∑ j ≠i δ t −1 j Lt −1 j
+
.
σ ii
Gσ ii
σ ii

(3')

While equation (3') is predicted by theory, the available data do not allow us to observe the
portion of loan stocks that are illiquid. We use total outstanding loans in period t-1, Lt-1i, in our
estimation equations instead of δt-1iLt-1i. Thus, the coefficient on outstanding loan stocks in our
estimations is not predicted to be exactly -1 as in equation (3'); instead, the coefficient will capture
the average effect of loan stock liquidity as well as the fact that losses on outstanding loan stocks
may not be perfectly correlated with losses on new loans.14
The degree to which outstanding loans are liquid or illiquid is not fixed but can change with
exogenous conditions. A downturn in a sector will reduce the liquidity of outstanding loans for two
reasons. First, borrowers in that sector are in worse shape, so they are more likely to try to roll over
their maturing loans. Second, because these loans are riskier, the bank faces greater adverse selection
problems when trying to sell or securitize the loans. While we cannot account for all liquidity
changes over time, our estimations do allow for a differential effect of loan stocks during sector
downturns.
In addition to the loan risk and liquidity effects described above, sector downturns may also
have a capital effect. A sector downturn may increase expected future losses on outstanding loans,
reducing a bank’s expected capital and making it effectively more risk averse. This capital effect
14

Following the model we would expect the estimated coefficient on outstanding loans from sector i to be the
average share of illiquid loans for the bank over the period. However, in addition to the fact there are other
considerations which affect loan supply, we will make several adjustments to our estimation equation (such as
estimating shares and not levels to avoid size effects) which change this prediction.

9

predicts that a downturn in one sector will decrease net lending changes in other sectors, especially
more liquid sectors, because banks can more easily shed risk in those sectors. To separately capture
the impact of such a correlation, we interact bank portfolio downturns with the risk aversion term.
4b. 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, NLC. Note that the stock of outstanding sector i loans Lti at the end of period t is the sum of
three items: the illiquid portion of the period t-1 loan stock, any retained liquid portion of the period
t-1 loan stock, and the new period t loans. Letting τti ∈ (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 Lti
equals (δti + τti(1-δti))Lt-1i + NLSti. We have
NLC ti = Lti − Lt −1i
= NLSti + [δ ti + τ ti (1 − δ ti )]Lt −1i − Lt −1i
= NLSti − [(1 − τ ti )(1 − δ ti )]Lt −1i

Net lending change is then the actual supply of new loans less the portion of liquid loan stocks that
are sold. Banks will sell or hedge some liquid loans if they can do so at fair prices, and will hold
some liquid loans either due to market imperfections or for strategic purposes. Regardless, banks will
tend to draw down or sell off the liquid portion of their outstanding loans more when their capital
falls (due to increased risk aversion) or if the portfolio risk associated with their liquid loans
increases (i.e., higher correlations with other loans). If the share of liquid loans, (1–δi)Lt-1i, is small
relative to the flow of new loans, or if the bank retains a large portion of its liquid loans—and both of
these conditions are more characteristic of small banks than of large banks—then NLC will be highly
correlated with new loan supply NLS.
4c. Specification
Equation (4) presents our basic estimation equation, which takes into account both the
unobservability of illiquid loans and new loan supply as well as the effects of sectoral downturns on
existing loan liquidity and new loan supplies. We also separate the risk tolerance measure G-1 from
the Sharpe ratio (pti-µti)/σti in order to better distinguish their effects.15 For ease of exposition, we
express equation (4) separately for each of the three loan sectors in the data—real estate, business,
and consumer. These adjustments result in the following set of estimation equations:

15

We have also done the estimation with the combined term and there are no significant differences in the
qualitative outcomes.

10

NLCt1 = − ∑ φi1 NLCti − ( β1 + γ 1 Dt1 ) Lt −1 1 − ∑ (( ρ i1 + λi1 Dti ) Lt −1i )
i = 2, 3

i = 2,3

p − µ t1
+ ( χ1 + ω1 DPt ) t1
+ (ξ1 + ς 1 DPt )Gt−1
σ 11
NLCt 2 = − ∑φi 2 NLCti − ( β 2 + γ 2 Dt 2 ) Lt −1 2
i =1, 3

−

(4.1)

∑ (( ρ i 2 + λi 2 Dti ) Lt −1i )

i =1,3

p − µt 2
+ ( χ 2 + ω 2 DPt ) t 2
+ (ξ 2 + ς 2 DPt )Gt−1
σ 22

(4.2)

NLCt 3 = − ∑ φi 3 NLCti − ( β 3 + γ 3 Dt 3 ) Lt −1 3 − ∑ (( ρ i 3 + λi 3 Dti ) Lt −1i )
i =1, 2

+ ( χ 3 + ω3 DPt )

i =1, 2

pt 3 − µ t 3
+ (ξ 3 + ς 3 DPt )Gt−1
σ 33

(4.3)

where i ranges from 1 to 3 indexing the three loan loan sectors mentioned above. Dti is an indicator
variable that equals one if there is a downturn in sector i during period t. DPt summarizes the effect
of downturns on the bank’s portfolio; it is a loan-share weighted average of the Dti indicator variables
for period t. Gt is the bank-specific risk aversion factor at the beginning of period t as described
above; its inverse Gt-1 is the bank’s risk tolerance. (pti–µti)/σii is the expected return-risk ratio (Sharpe
ratio) for sector i loans. The coefficients φ, β, γ, ρ, λ, χ, ω, ξ, and ζ are parameters to be estimated.
The coefficients on the net lending change and loan stock variables (φ, β, γ, ρ, and λ) absorb the
effects of the correlation and variance terms, σij/σii, present in (3) but absent here. The coefficients on
loan stocks also absorb the unobservable liquidity effects discussed above.
We estimate equation (4) separately for each of the three loan sectors, controlling for fixed
bank effects, quarterly effects, and using two stage least squares (2SLS) to account for the
endogeneity or simultaneity of the net lending change variables, NLCit. Our approach differs from
prior research on the determinants of loan supply (net lending) changes by focusing on the impact of
past and current portfolio decisions (existing loan stocks in the same sector, existing loan stocks in
other sectors, and new lending in other sectors) and by distinguishing loan stock effects in normal
times (Dti=0 ∀ i) from loan stock effects during sector downturns (Dti≠0 for at least one i) when we
expect these stocks to be less liquid.
4d. 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 a given sector, net lending change will be negatively related

11

to overhang (βi<0). This negative overhang effect will be stronger for sectors that are less liquid;
for example, if sector i loans are less liquid than sector j loans, then βi<βj<0.
•

Same-sector downturns: Within a given sector, downturns will increase loan illiquidity and
bank risk aversion, and as a result banks will desire to shed loans in that sector (γi<0).

•

Cross-sector loan overhang: If the portfolio model is the primary determinant of net lending
changes, then the impact of cross-sector loan overhang on net lending change (ρji) will be
increasingly negative (or less positive) as the covariance between loan losses in sectors i and j
increases. Holding covariance constant (and not equal to zero), the magnitude of ρji will be larger
the more illiquid is loan stock j.

•

Cross-sector downturns. All else equal, a downturn in sector j will both increase loan illiquidity
in that sector and make the bank more risk averse due to expected reductions in capital. The
illiquidity effect increases loan overhang in sector j and amplifies the effect of the loan stock on
the net lending change (i.e., λji should have the same sign as ρji). The risk aversion effect will
cause the bank to shed loans in all sectors, including sector i (λji<0 regardless of the sign of ρji),
and will be larger if the loans in sector i are more liquid. The net effect will depend upon whether
these two effects reinforce or offset one another and, in the latter case, which factor dominates.

•

Cross-sector net lending change: If our model holds strictly, the estimated effect of net lending
change in sector j on net lending change in sector i (φji) should be the same sign as the estimated
effect of sector j loan stocks on net lending change in sector i (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 lending
change in sector i.

•

Risk-adjusted profits and risk tolerance: Within a given sector, net lending change will increase
with the return-risk ratio (χi>0) and with the bank’s risk tolerance (ξi>0). Both of these effects
will be dampened by increased portfolio exposure to downturns, which reduce capital and make
the bank more risk averse (ωi,ζi <0).

5. Data and Variables
We estimate equation (4) for three categories of loans: real estate loans, business loans, and
non-credit-card consumer loans, using quarterly data on small commercial banks from the Federal

12

Reserve’s Report of Condition and Income (Call Report) for the period 1987:4 to 2002:4.16 The data
exclude banks with less than $25 million in assets in current dollars (the Call Reports require very
little detail for banks below this size) and exclude banks with more than $1 billion in assets in real,
2000 dollars. This $1 billion threshold is a typical cut-off for defining community banks (DeYoung,
Hunter, and Udell 2004), and it retains over 90% of all U.S. commercial banks during our sample
period. Although the Call Report data offer somewhat greater detail on the loan portfolios of larger
banks, small banks are attractive for our purposes because their loans tend to be less liquid than those
of larger banks.
The limited lending capacity of small banks precludes them from making loans (or from
participating in 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.
Similar considerations apply to consumer lending, where asset securitization has driven a
wedge between small banks and large banks. Origination and securitization of consumer loans (e.g.,
credit card or automobile loans) impose a number of fixed costs on the lender, including legal and
credit rating agency fees, overhead for performing statistical analysis, costs of establishing a
reputation in the asset-backed securities market, and the ability to provide ‘credit enhancements’
(e.g., retain a portion of the loans’ credit risk) to the buyers of the asset-backed securities. The result
is that consumer loans are relatively liquid when made by large banks that operate at the scale needed
to efficiently participate in securitized consumer lending, but are relatively illiquid when made by
small banks that cannot. The relative illiquidity of business loans and consumer loans at small banks
suggests that, all else equal, risk overhang will be a bigger concern for small banks than for large
banks.
Although commercial real estate lending by small banks suffers from the same illiquidity as
does their business lending, their residential real estate lending is relatively liquid. Most home

16

We exclude credit card loans because nearly all small banks exited this line of business during our sample period,
due to new production processes (i.e., credit scoring and loan securitization) that exhibit huge scale economies. The
Call Reports also include data on a number of other loans (e.g., loans to government entities, loans to other financial
institutions), but these loans comprise a negligible portion of the loan portfolios of small banks.

13

mortgage securitizations are done through government-sponsored enterprises (GSEs) which take on
the fixed costs just mentioned, and typically do not involve explicit credit enhancement by the
originating bank. Thus, to the extent a small bank’s real estate lending is residential in nature, risk
overhang may be a lesser issue in this sector.
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. Also, because
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), 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 for large banks. Furthermore, during our
period of investigation, small banks are less likely to be involved in mergers that significantly alter
their business strategies. And finally, as most small banks lack the expertise to hedge credit and other
risks with off-balance sheet derivative securities, balance-sheet-based measures may be a more
accurate measure of a small bank’s capacity for bearing risk than they would be for a larger bank.
Table 1 presents the definitions of the variables we use to specify and estimate equation (4).
Real estate loans, LRE, include commercial development loans and mortgages on farmland, single
family homes, and multi-family dwellings. Business loans, LBUS, include all commercial and
industrial loans; for banks located in rural markets LBUS also includes agricultural production loans.
Consumer loans, LCON, include all revolving, installment, or single payment loans to individuals
(e.g., auto loans, students loans, personal lines of credit). Our dependent variable NLCit, the net
lending change in sector i lending in quarter t, is measured 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 net lending change variables and all loan stock variables by
dividing them by beginning-of-quarter assets.
We construct the Sharpe ratio as the expected profit for loan type i at each bank for each
period t, divided by the profit variance of loan type i over the sample period. Expected profit is the
expected percent return (the bank’s interest and fee income from loan sector i during period t divided
by its stock of accruing loans at the end of period t) multiplied by the expected performance of loans
in sector i (the historical percentage of accruing loans in sector i) minus the average deposit rate paid

14

by the bank (the interest paid on deposits during period t divided by the average deposits in the
current and prior period).17 The profit variance of loan type i is measured as the variance of the
quarterly change in expected profit in sector i for the whole sample period, calculated separately for
urban and rural banks in each state.18
Bank specific risk tolerance, G-1, is measured as total equity capital divided by total assets.
Intuitively, banks with lower financial leverage (higher equity capital) will in general be more risk
tolerant in their lending decisions because they are better able to absorb loan losses (and the attendant
reductions in equity capital), and are also better able to sustain increased illiquidity in any one loan
sector without making compensating adjustments in the other portions of their loan portfolio.19 Our
indicator variable for a sectoral downturn in loans is NPpoor, which equals one in quarters for which
the average ratio of nonperforming loans to assets across all banks in a geographic market (MSA for
urban banks, nonMSA counties within the state for rural banks) is in the highest quartile of the
sample distribution for that market during our sample period. We measure the combined effect of
sectoral downturns on a bank’s portfolio with the variable NPport, which is a loan-weighted sum of
the sectoral indicator variables NPpoori. (The NPport risk measure may be a more conditional
measure of risk than the whole-sample estimate of profit variance in the Sharpe ratio, and thus may
be more relevant for explaining net lending change in the short-run.)
If banks manage their different types of loans as a portfolio of loans, then the net lending
changes in sectors j≠i on the right-hand-side of equation (4) will be endogenous to the dependent
variable, the net lending change in sector i. We use several measures of endogenous sector j supply
effects as instruments to identify the equation.20 These include the expected profit term ptj–µtj for the
relevant endogenous variable, as well as a number of predictors of local economic conditions
identified in Daly, Krainer and Lopez (2003) and Crone (2003): Crone’s regional index, the change
17

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.
18
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.
19
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.
20
Any variable that is correlated with the right-hand-side endogenous variables but not correlated with the errors in
the banks’ loan supply decisions will be useful for identifying the equation. We use standard two-stage least squares
(2SLS) techniques, first regressing loan changes on measures of local economic conditions along with excluded
variables from the other equations, and then using these results to create fitted values for use in the second stage
regressions, which correspond to equation (4).

15

in this index, and state-level measures of personal income growth, employment growth,
unemployment growth, the unemployment rate, and the growth in housing prices.21
Since our goal is to examine banks’ portfolio decisions and the manner in which banks trade
off new loans given outstanding loan stocks, we only consider banks that engage in substantial
amounts of all three types of lending—real estate, business and consumer—and specialize in none of
them.22 We define these ‘nonspecialist’ lenders as banks that have at least 5 percent of assets invested
in real estate loans and at least 3 percent of assets invested in business loans and in consumer loans.
We also omit banks with over 65 percent of assets invested in real estate loans or over 50 percent of
assets invested in either business loans or consumer loans.23 We selected these thresholds primarily
to exclude banks doing little or no lending in a given category, since these banks would not be
considering the trade-offs between all three loan categories. Indeed, the minimum thresholds are
binding far more often than the maximums: about 92% of the observations that do not meet these
standards fall below the minimum thresholds. In all, about 25% of the observations fail to meet either
the minimum or maximum thresholds.
We make several additional data adjustments to avoid the effects of data errors, merging
banks, or banks with an abrupt change in strategy. The data from small banks can be very noisy.
Thus, we delete bank-quarter observations where 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. We also omit bank-quarter observations when banks have negative
equity, bank-quarter observations in which the assets of another bank are acquired, and all

21

The Federal Reserve Bank of Philadelphia’s Consistent Economic Indexes for the 50 states are available at:
http://www.phil.frb.org/econ/stateindexes/index.html. Personal income growth data come from the Bureau of
Economic Analysis, employment and unemployment data are from the Bureau of Labor Statistics, and the housing
price data are from the Office of Federal Housing Enterprise Oversight. All series have been adjusted for quarterly
effects by using residuals from a regression on quarterly indicator variables.
22
When we estimate equation (4) for all banks—including those that specialize in one category of lending as well as
those that manage a more diversified portfolio—the estimated effects of the endogenous net lending changes NLCt,i≠i
and loan stocks Lt-1,j are much less consistent. This is not surprising since it is quite likely that a bank that specializes
in just one type of loans—say, business loans—practices most of its on-balance sheet portfolio risk management
across loans within the business loan category (which the data do not allow us to observe) rather than across all three
observable loan categories. The fact that the data preclude us from testing for on-balance sheet portfolio risk
management within loan categories does not invalidate our tests for this behavior across loan categories.
23
We used higher upper and lower thresholds for real estate loans because they comprise a larger percentage of
assets for the average small bank in the U.S. (about 25% at year-end 1989 and 35% at year-end 1999) than consumer
loans (about 11% and 8%) or business loans (about 11% and 10%). A higher proportion of rural banks fall below the
minimum real estate and business loans thresholds, while a higher proportion of urban banks fall below the
minimum consumer loans threshold. Varying the thresholds somewhat does not significantly change our results.

16

observations from banks that never lend more than 15% of their assets.24 Given these constraints,
our dataset begins with 322,236 bank-quarter observations.
We estimate the model separately for banks located in urban markets (banks located in
MSAs) and banks located in rural markets (outside of MSAs) for several reasons. First, rural banks
typically face less competition and often have considerable local market power. With greater rents at
stake, their ability and willingness to absorb risk and overhang may differ markedly from those of
urban banks. Second, a large percentage of business loans at rural banks are made to agricultural
businesses, mostly to small farms. For rural banks, we include agricultural production loans (which
banks report in a separate category in the Call Reports) in our business loans. Small farm financing is
often a mixture of operating loans to the business, real estate loans for the farm home, and consumer
loans to purchase vehicles and other services used primarily in farm production. Thus, the precise
nature of, and correlations between, the three loan sectors are likely to be different for rural banks as
compared with urban. Previous research shows that rural banks hold relatively low levels of total
loans, relatively high levels of marketable securities, and relatively high levels of equity compared to
similarly sized urban banks (DeYoung, Hunter, and Udell, 2004), consistent with a less sophisticated
approach to risk management.

Table 2 presents summary statistics for the data and variables used in our regression
analysis. The top panel reports statistics for rural banks, the bottom for urban banks. The number
of observations falls to 189,650 bank-quarters (69,013 for urban banks; 120,323 for rural banks)
due to lags required to calculate variables and missing data. (For example, our expected profit
calculations require at least three consecutive prior quarters of profit data.) On average, rural
banks are significantly smaller than urban banks in terms of total assets and hold proportionally
fewer assets in real estate loans, more assets in business (including agricultural production)
loans, and similar amounts of assets in consumer loans.

6. Estimation Results

Table 3 presents our equation (4) regression results describing quarterly net lending
changes in real estate (panel A), business (panel B) and consumer (panel C) loans. We performed
separate estimations for rural banks and urban banks, and with and without the indicator dummy

24

While it might be desirable to keep banks with negative equity, negative equity poses potential problems for using
bank equity capital to measure bank risk tolerance. Since banks with negative equity account for very few
observations, excluding these is unlikely to affect the estimation in a significant way.

17

variables for sectoral downturns (NPpoor) and portfolio downturns (NPport) described above.
All of the regressions include bank-specific fixed effects and seasonal (quarterly) controls.
The results in table 3 are substantially consistent with our predictions, and strongly suggest
that small commercial banks make net lending change decisions in a manner that is consistent with
optimal risk management and capital budgeting. The estimated coefficients on the same-sector
overhang variables (Li,t-1) are all negative and statistically significant, as expected. Moreover, these
coefficients tend to be larger in magnitude for more illiquid types of loans. For rural banks, the
estimated same-sector overhang effect for real estate lending (-.007 or -.009) is smaller in magnitude
than the same-sector effect for consumer lending (-.033 or -.030), which in turn is smaller in
magnitude than the same-sector effect for business lending (-.102 or -.104). The ordering is less strict
for urban banks, where the same-sector real estate and consumer loan effects are relatively small but
quite similar in magnitude (-.026 versus -.026 or -.024, respectively), while the same-sector business
lending effect is relatively larger in magnitude (-.084 or -.082). In all cases this risk overhang effect
is strongest for business loans—not surprising given that the small banks tend to make business loans
to small, privately owned firms, and the informational opacity of these borrowers makes their loans
substantially less liquid on average than the other types of loans. The magnitudes are non-trivial—for
example, a 10 percent increase in business loan “overhang” at the average urban bank is associated
with an approximate 8/10ths percent reduction in business loan share during the following quarter.25
The estimated effects of a same-sector downturn (Li,t-1*NPpoori,t) tend to have the expected
negative sign: in general, we expect loan stocks to become more illiquid during a sector downturn,
which would reinforce the negative same-sector loan overhang coefficients just discussed. This is
always the case for the urban banks. For rural banks the results are mixed: a significant negative
coefficient (suggesting increased illiquidity) for consumer loans, a non-significant coefficient for real
estate loans, and a significant positive coefficient (suggesting reduced illiquidity) for business loans.
The positive sign likely reflects institutional factors. As farmers’ creditworthiness deteriorates in a
rural downturn, many become eligible for subsidized government loan programs that provide the
bank with loan loss guarantees. The presence of these government loan programs—which in effect
reduces the riskiness and the illiquidity of these loans—coupled with farmers’ increased demand for
credit during downturns, act to dampen rather than exacerbate the same-sector loan overhang effect.

25

Multiplying the same-sector loan overhang coefficient (-.084) by a ten percent change in mean business
loans/assets (.0113) and dividing by mean business loans/assets yields the result. While this effect only partially
offsets the current period overhang in business loans, additional reductions would continue in following quarters,
ceteris paribus.

18

Since our real estate loan variable contains farm mortgages, these same institutional factors may
be causing the non-significant coefficient on the same-sector real estate downturn for rural
banks. This interpretation is supported by the fact that we do not observe these anomalies in the
urban bank regressions.
The magnitudes of the same-sector downturn effects are consistent with known differences in
the nature of the bank-borrower relationship across loan categories. The estimated coefficient on
Li,t−1*NPpoori,t for business loans is the least negative (or most positive) of the three same-sector
downturn effects for both urban banks (-.005 versus -.008 and -.011), respectively, for real estate and
consumer lending) and rural banks (.006 versus -.001 and -.008). Thus, even though business loans
tend to be more risky and less liquid than the other loan types, small banks’ sensitivity to risk
overhang remains relatively unaffected by business sector downturns. This suggests that small banks
measure the value of their relationships with business clients across the business cycle, and are
willing to accept temporary increases in risk and illiquidity in order to maintain the business
relationship throughout the downturn. Indeed, credit access during downturns is a crucial component
of a banking relationship for small business firms. Moreover, because small banks’ business loans
are very illiquid to begin with, a downturn may not increase this much further.
As expected, the estimated coefficients on the Sharpe ratio are positive and all are
statistically significant. This is a supply effect: banks increase their net lending when the riskadjusted expected returns from lending increase. This supply effect is stronger during economic
downturns, as indicated by the positive coefficients on the Sharpei,t*NPporti,t variable. During
economic downturns, net lending becomes more responsive to increases in expected profitability,
perhaps because higher expected profitability increases capital. This effect tends to be small,
however—the only exception being the relatively large estimated coefficient (.004) for business
lending at urban banks, again suggesting an important countercyclical role for small commercial
banks.
The results for the risk tolerance variable (G-1) are less straightforward than we had expected,
but nonetheless consistent with optimal portfolio risk management. As expected, the risk tolerance
coefficients are positive for business lending—but these coefficients are unexpectedly negative and
significant for real estate lending, and are generally non-significant for consumer lending. Thus,
holding constant existing loan mix and net lending changes in other sectors, increased risk tolerance
at both urban and rural banks is manifested by movements out of relatively liquid loans (real estate,
mostly home mortgages) and into relatively risky, illiquid loans (business). Economic downturns

19

have little impact on these findings, as indicated by the estimated coefficients on G−1*NPport which
are statistically non-significant in five of six cases. We explore this finding further in our subsample
estimates below.
Although we have no a priori expectation about the coefficient signs on the cross-sector loan
stock (Lj≠i,t-1) or net lending change (NLCj≠i,t-1) variables, we do expect these coefficients to have the
same sign for a given loan type. We obtain this result more often than not: of the 24 pairs of crosssector coefficients in the Table 3 regressions, 13 pairs have the same statistically significant sign
while only six pairs have statistically significant opposite signs. Moreover, the large majority of the
individual cross-sector coefficient estimates (34 out of 48) are positive and significant; based on our
theoretical model (see equation (3) above) this implies that bank lenders act as if loan shocks covary
negatively among pairs of loan types included in our data. The most systematic of these relationships
is for business and real estate lending: in Panel A (real estate NLC) all eight of the cross-sector
coefficients for business loans are positive and significant, while in Panel B (business NLC) all eight
of the cross-sector coefficients for real estate loans are also positive and significant. The results also
imply, although less systematically, that bank lenders expect business loans and consumer loans to
covary negatively: the cross-sector coefficients linking these two types of lending (the cross-sector
coefficients on consumer loans in Panel A and real estate loans in Panel C) are positive and
significant in 10 out of 16 cases, and negative and significant just twice. The weakest evidence of
cross-sector effects is for real estate lending and consumer lending (consumer loans in Panel A and
real estate loans in Panel C), for which the cross-sector coefficients are positive and significant in just
eight cases but negative and significant in five cases. These results are economically reasonable, as
they suggest that shocks to household loans (consumer loans and real estate loans, which at small
banks are predominantly home mortgages) tend to move together, while shocks to business sector
loans and household sector loans do not.
As a robustness test we checked to see whether the loan covariances implied by our Table 3
estimates of bank loan portfolio behavior are consistent with the actual loan covariances in the raw
data. Using the raw data on expected profits for real estate, business, and consumer loans (i.e., the
numerators in our Sharpe ratios), we calculated variance-covariance matrices at the bank-level, and
then aggregated up to produce an average variance-covariance matrices for both urban and rural
banks. Although all of the average expected profit covariances are positive, their relative magnitudes

20

are consistent with our regression estimates.26 For example, the smallest positive covariances are
between real estate loans and business loans, consistent with the diversification opportunities implied
by our cross-sector parameter estimates for this pair of loans. In contrast, the largest covariances are
between consumer loans and real estate loans, consistent with the weak cross-sector results in our
regressions for this pair of loan types. Our calculations are also consistent with the relative ordering
of our estimated same-sector risk overhang results: the raw data variance for expected profits is
largest for business loans and smallest for real estate loans.27
6a. Subsample estimations
Over the twelve years of our estimation period, improvements in financial technology and
information flows (e.g., automated loan underwriting, loan securitization) have deepened the
secondary market for loans—for small banks this has been especially relevant for home mortgage
loans, which have become increasingly liquid investments. To examine the impact of these
developments on loan overhang and portfolio risk management, we re-estimated equation (4)
separately for an early sub-period (1990 through mid 1996) and a late sub-period (mid 1996 to 2002).
The results are displayed in Table 4. Overall, the estimated model parameters for the two sub-periods
are very similar in signs and significance to the full-sample estimates in Table 3, with the following
notable exception: the results suggest that loan overhang effects have grown weaker over time,
perhaps in response to increases in the liquidity of consumer and real estate loans.
In both the real estate and consumer NLC regressions (Panels A and C) the estimated risk
tolerance coefficients change from largely positive or positive and non-significant in the early period
to largely negative and significant in the later period. In contrast—and consistent with the full-sample
results—the risk tolerance coefficients are always positive in the business NLC regressions (Panel
B). Thus, the early period results are consistent with our original expectations that increased risk
tolerance (i.e., extra equity capital) is associated with increased net lending across the board, while in
the later period our results suggest that banks respond to increased risk tolerance by shifting their net
lending out of relatively less risky (and increasingly liquid) real estate and consumer loans and into
relatively more risky business loans. The estimates also suggest more straightforward patterns of risk
management and portfolio diversification in the early sub-period that are consistent with generally

26

For urban banks the average covariances of expected profits are 0.00009 (real estate-business), 0.00011 (businessconsumer), and 0.00014 (consumer-real estate). For rural banks these same covariances are 0.00013, 0.00013, and
0.00017, respectively.
27
For urban banks the average variances of expected profits are 0.00071 for business loans, 0.00022 for consumer
loans, and 0.00016 for real estate loans. For rural banks these same variances are 0.00041, 0.00022, and 0.00018,
respectively.

21

less liquid loan stocks: the same-sector loan overhang coefficients tend to be larger (i.e., more
negative) and the estimated cross-sector coefficients are always positive in the early period.
We also investigated whether banks in multi-bank holding companies (MBHCs) managed
their loan portfolios differently than independent banks. Multi-bank organizations may manage
their loan portfolios at the holding company level rather than at the bank level, possibly
facilitated by internal capital markets—if so, we would expect to find generally weaker evidence
of loan overhang and risk sensitivity in our regressions for banks affiliated with these
organizations. To examine this possibility, we re-estimated equation (4) for a sub-sample of
quarterly observations of banks that were MBHC members either in every quarter of the data or
in every post-1989 quarter. The results are displayed in Table 5 and offer little evidence that loan
portfolios in these banks are managed at the organization level.
For example, compared the full-sample results in Table 3 (first and third columns), 11 of
the 18 same-sector and cross-sector loan overhang coefficients are statistically significant and
larger. Similarly, 5 of the 6 coefficients on both the Sharpe variable and the risk tolerance
variable are statistically significant and larger than in Table 3. These results imply that loan
portfolios are managed at the local bank level, not at the organization level, which is consistent
with the relationship-based nature of many of the loans made by community banks. Given this
local focus, the results also imply that affiliate bank managers face especially strong incentives
to manage portfolio risk, perhaps because the monitoring and performance management
environment in these organizations is stronger than in independent banks, many of which are
family-owned and managed (DeYoung, Spong, and Sullivan 1999). If there are functioning
internal capital markets within these multi-bank organizations, their impact on investment
decisions appears to be minimal.

7. Conclusion and Discussion
In this paper we use a portfolio model of bank lending to examine how existing loan stocks,
net lending decisions, financial leverage, exogenous shocks to loan quality and capital, and loan
sector profitability affect the net lending decisions of small commercial banks for a 13-year period,
1989:Q4-2002:Q4. We document that small banks lend in a manner that is generally consistent with
optimal risk management and capital budgeting under costly external finance. For these banks’
shareholders, this suggests that banks are managing their capital and asset portfolios in a manner that

22

reduces the chances that the bank will find itself with too little capital to fund attractive projects in
the future. Our evidence suggests that this management is performed at the (separately capitalized)
bank level; we find little evidence consistent with internal capital markets.
Our results also have implications for the dynamics of bank lending. All else equal, our
results indicate that banks allocate capital toward loan sectors with the highest risk adjusted returns,
where it will be most productive. But during sector downturns, we find that banks systematically
reduce credit supply not only to borrowers in that sector, but also to borrowers in other sectors. In
addition, the supply-increasing effect of an increase in expected profitability is smaller during sector
downturns, perhaps because downturns increase the credit risk of both outstanding loan stocks and
new loans alike.
At a theoretical level, our model and results suggest that pro-cyclic lending arises out of
changes in bank lending capacity based on bank capital, loan illiquidity and effective risk aversion.
In this respect, it is closest to the model of Holmstrom and Tirole (1997), who focus on the effect of
bank capital on bank lending. Nevertheless, we go beyond their model by predicting and
demonstrating the impact of loan illiquidity and loan overhang. These results are generally consistent
with the models of Froot and Stein (1998) and Gron and Winton (2001).
Our findings also have policy implications for the supply of bank credit to households and
small businesses and macroeconomic activity. We show that shocks to bank capital and loan
portfolios reduce lending; since shocks to small banks’ asset portfolios generally come from shocks
to local economic activity, this implies that bank lending will be pro-cyclical. If bank lending
becomes more profitable (a positive shock), banks will increase their lending capacity and risk
tolerance as their equity increases, and this will be further enhanced by the relatively liquid nature of
well-performing loans. As local economic activity continues to expand, at some point banks will
compete for more business by providing loans to more risky borrowers or by providing loans to
borrowers at lower interest rates. When local economic activity in a particular sector begins to slow,
banks’ loan portfolios in that sector will begin to deteriorate. Defaults will directly reduce bank
capital and lending capacity and, as our results highlight, bank lending will be further reduced by the
effects of loan overhang as outstanding loans in the depressed sector become more risky and less
liquid.
This effect will be moderated if the bank holds a significant portion of its loans in sectors
whose shocks are less positively correlated with the sector experiencing the downturn. In our data,
banks were able to achieve such diversification by lending both in the business sector and in the
consumer and/or real estate sectors. As such, our model suggests that there may be welfare gains

23

from improved bank diversification. We also find that the effects of economic downturns are more
moderate in the small business loan sector, perhaps because banks have greater incentives to preserve
the value of these lender-borrower relationships across the business cycle.
Nevertheless, a caveat is in order. Our paper has focused on the behavior of small and
relatively diversified banks; large banks or more specialized banks may behave differently. For
example, large banks may be able to use alternative risk management techniques to reduce overhang
effects. 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
procyclical way, exacerbating the effects we have found. These issues remain to be tested.

24

References
Beatty, Anne, and Anne Gron (2001), “Capital, Portfolio, and Growth: Bank Behavior Under RiskBased Capital Guidelines.” Journal of Financial Services Research 20:1, 5-31.
Berger Allen N. and Gregory Udell (1994), “Did Risk-Based Capital Allocate Bank Credit and Cause
a ‘Credit Crunch’ in the U.S.?” Journal of Money, Credit and Banking 26, 585-628.
Berger, Allen, Anthony Saunders, Joseph Scalise, Gregory Udell (1997) “The Effects of Bank
Mergers and Acquisitions on Small Business Lending,” Wharton Working paper
Berger, Allen, Richard Rosen, Gregory Udell, (2001) “The effect of market size structure on
competition: the case of small business lending,” October.
Berger, Alan, Nathan Miller, Mitchell Petersen, Raghuram Rajan, Jeremy Stein (2005) “Does
function follow organizational form? Evidence from the lending practices of large and small
banks.” Journal of Financial Economics 76(2), 237-269.
Berger, Allen, and Gregory Udell, (2003) “The Institutional Memory Hypotheses and the
Procylicality of Bank lending Behavior,” working paper April.
Berger, Allen, Iftekar Hasan, and Leora Klapper, (2004) “Further Evidence on the Link Between
Finance and Growth: An International Analysis of Community Banking and Economic
Performance” Journal of Financial Services Research 25(2/3), 169-202.
Bernanke, Ben and Cara Lown (1991), “The Credit Crunch.” Brookings Papers on Economic Activity
2, 205-247.
Besanko, David, and George Kanatas (1996), “The Regulation of Bank Capital: Do Capital
Standards Promote Bank Safety?” Journal of Financial Intermediation 5:2 (April), 160-183.
Bitler, Marianne P., Alicia M. Robb, and John D. Wolken (2001), “Financial Services Used by Small
Businesses: Evidence from the 1998 Survey of Small Business Finances,” Federal Reserve
Bulletin, vol. 87, pp. 183-205.
Boyd, John, and Stanley Graham (1991), “Investigating the Banking Consolidation Trend.” Federal
Reserve Bank of Minneapolis Quarterly Review 15:2 (Spring), 3-15.
Brinkman, Emile J. and Paul M, Horvitz (1995), “Risk-Based Capital Standards and the Credit
Crunch.” Journal of Money, Credit and Banking 27, 848-863.
Crone, Theodore, (2003), “Consistent Economic Indexes for the 50 states,” working paper, Federal
Reserve Bank of Philadelphia, June.
Daley, Mary, John Krainer and Jose Lopez (2003) “Does Regional Economic Performance Affect
Bank Conditions? New Analysis of an Old Question,” working paper, Federal Reserve Bank
of San Francisco, November.

25

DeYoung, Robert, William C. Hunter, and Gregory F. Udell (2004, forthcoming), “The Past, Present,
and Probable Future for Community Banks.” Journal of Financial Services Research 25(2/3).
DeYoung, Robert, Kenneth Spong, and Richard J. Sullivan, (2001), “Who's Minding the Store?
Motivating and Monitoring Hired Managers at Small Closely Held Commercial Banks,” Journal
of Banking and Finance 25: 1209-1244.
Diamond, Douglas and Raghuram Rajan (2000), “A Theory of Bank Capital,” Journal of Finance 55,
2431-2465.
Froot, Kenneth, and Paul O’Connell (1999), “The Pricing of U.S. Catastrophe Reinsurance.” In
Kenneth Froot (ed.), The Financing of Catastrophe Risk, University of Chicago Press,
London.
Froot, Kenneth, David Scharfstein, and Jeremy Stein (1993), “Risk Management: Coordinating
Corporate Investment and Financing Policies.” Journal of Finance 48:5 (December), 16291658.
Froot, Kenneth and Jeremy Stein (1998), “Risk Management, Capital Budgeting, and Capital
Structure Policy for Financial Institutions: An Integrated Approach.” Journal of Financial
Economics 47:1 (January) 55-82.
Gorton, Gary, and Andrew Winton (2003), “Financial Intermediation.” In George Constantinides,
Milton Harris, and Ren Stulz (eds.), Handbooks in the Economics of Finance, Volume 1A:
Corporate Finance, Elsevier Science, Amsterdam.
Gron, Anne, and Andrew Winton (2001), “Risk Overhang and Market Behavior.” Journal of
Business 74:4 (October), 591-612.
Hall, Brian (1993), “How Has the Basel Accord Affected Bank Portfolios?” Journal of the Japanese
and International Economies 7, 408-440.
Hancock, Diana and James A. Wilcox (1993), “Has There Been a ‘Capital Crunch’ in Banking? The
Effects on Bank Lending of Real Estate Market Conditions and Bank Capital Shortfalls.”
Journal of Housing Economics 3, 31-50.
Hancock, Diana and James A. Wilcox (1994a), “Bank Capital, Loan Delinquencies, and Real Estate
Lending.” Journal of Housing Economics 3, 121-146.
Hancock, Diana and James A. Wilcox (1994b), “Bank Capital and the Credit Crunch: The Roles of
Risk-Weighted and Unweighted Capital Regulation.” Journal of the American Real Estate
And Urban Economics Association 22, 59-94.
Haubrich, Joseph and Paul Wachtel (1993), “Capital Requirements and Shifts in Commercial Bank
Portfolios,” Federal Reserve Bank of Cleveland Economic Review 29, 2-15.
Holmstrom, Bengt and Jean Tirole (1997), “Financial Intermediation, Loanable Funds, and the Real
Sector.” Quarterly Journal of Economics 112, 663-691.

26

Marcus, Alan (1984), “Deregulation and Bank Financial Policy.” Journal of Banking and Finance 8,
557-565.
Peek, Joe and Eric Rosengren (1995), “The Capital Crunch: Neither a Borrower Nor a Lender Be.”
Journal of Money, Credit and Banking 27, 625-638.
Petersen, Mitchell and Raghuram Rajan, (1994) “The benefits of lending relationships Evidence
from small business data,” The Journal of Finance vol. 49, no. 1, march, pp. 3-37.
Petersen, Mitchell and Raghuram Rajan, (2000) “Does Distance Still Matter? The Information
Revolution in small business Lending” working paper.
Sharpe, Steven (1995), “Bank Capitalization, Regulation, and the Credit Crunch: A Critical Review
of the Research Findings.” Finance and Economics Discussion Series Paper No. 95/20, Board
of Governors of the Federal Reserve System.
Thakor, Anjan (1996), “Capital Requirements, Monetary Policy, and Aggregate Bank Lending:
Theory and Empirical Evidence,” Journal of Finance 51:1 (March), 279-324.

27

Table 1: Variable Definitions

Net lending change

Variable
Name
NLCit

Outstanding loan stock

Lit-1

Risk tolerance

Gt-1

Sharpe ratio

Sharpeit

Expected profit

pit - µit

Variance of shocks

σii

Nonperforming loan ratio

NPLit

Sectoral downturn

NPpoorit

Sectoral downturn effect
on bank portfolio

NPportt

Variable

Description

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.
The loan stock in sector i at the end of period t-1, normalized
by bank assets.
Bank equity capital divided by bank assets at end of period t-1.
Expected profit for loans in sector i in period t divided by the
variance of ‘shocks’ to loan sector i divided by 100.
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).
The variance of the expected profit in sector i over the full
sample period, calculated at the market level, where markets
are defined as MSAs for urban banks and as the in-state, nonMSA county average for rural banks.
Nonperforming loans in sector i in period t divided by sector i
loan stock at the end of the prior period.
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.
A loan-share weighted average of the NPpoorit indicator
variables in period t. The shares are the beginning of period
loans to total assets for the three types of loans.

Notes: In the definitions above, “end of period t-1” is identical to “beginning of period t.” Unless
otherwise noted, all data are from the Call Reports. Employment growth numbers are from Bureau of
Labor Statistics, Employment (Payroll) Survey. All variables except NPpoorit and σii are bank-specific;
we have omitted the bank subscript for simplicity.

28

Table 2: Sample Statistics
Variable
RURAL BANKS
number of quarters
Assets
NLCRE
NLCBUSAG
NLCCON
RE loans/ assets
BUSAG loans/assets
CON loans/ assets
SharpeRE
SharpeBUSAG
SharpeCON

Gt-1
Expected RE profit
Expected BUSAG profit
Expected CON profit
URBAN BANKS
dataq
Assets
NLCRE
NLCBUS
NLCCON
RE loans/ assets
BUS loans/assets
CON loans/ assets
SharpeRE
SharpeBUS
SharpeCON

Gt-1
Expected RE profit
Expected BUSAG profit
Expected CON profit

Obs

Mean

Median

Std. Dev.

Min

Max

120,323
120,323
120,323
120,323
120,323
120,323
120,323
120,323
120,323
120,323
120,323
120,323
120,323
120,323
120,323

30.05
93533.77
0.007
0.003
0.001
0.306
0.165
0.094
4.787
0.892
1.490
0.099
.012
.031
.015

30
66158
0.005
0.002
0.001
0.300
0.144
0.081
5.002
0.672
1.423
0.093
.012
.029
.015

14.73
85943.76
0.017
0.019
0.008
0.123
0.095
0.053
2.494
0.719
1.065
0.027
.005
.019
.010

5
25002
-0.226
-0.260
-0.185
0.033
0.005
0.0004
-9.276
-0.121
-2.530
0.005
-.017
-.007
-.017

56
1033720
0.287
0.222
0.353
0.745
0.731
0.478
19.525
8.136
11.524
0.317
.038
.207
.102

69,013
69,013
69,013
69,013
69,013
69,013
69,013
69,013
69,013
69,013
69,013
69,013
69,013
69,013
69,013

28.64
162354.4
0.009
0.002
0.001
0.350
0.113
0.099
3.698
0.318
1.332
0.090
.012
.034
.017

28
103362
0.007
0.002
0.0005
0.349
0.097
0.080
3.599
0.233
1.175
0.001
.013
.024
.015

14.58
160919.6
0.021
0.015
0.010
0.121
0.066
0.066
2.383
0.296
0.986
0.024
.006
.029
.012

5
25044
-0.386
-0.389
-0.193
0.038
0.007
0.005
-7.065
-0.106
-1.958
0.002
-.017
-.007
-.017

56
1044676
0.364
0.333
0.231
0.716
0.546
0.532
21.065
5.580
13.014
0.350
.036
.335
.105

Notes: All variables are from the Call Reports, and defined in Table 1. RE is real estate, BUSAG is
business and agricultural (reported for rural only), BUS is business (reported for urban only), and CON
is consumer. The loan-to-assets ratios and the Gt-1 variables are measured at the beginning of the
period.

29

Table 3: Instrumental Variables Regression with Bank Fixed Effects and Seasonal Controls*
Panel A: Dependent Variable Net Change in Real Estate Lending
RURAL
0.269***
0.275***
NLCBUS,t
NLCCON,t
LRE,t-1 (same-sector)

(0.016)

(0.069)

(0.07)

0.194***

0.130***

0.001

-0.053

(0.041)

(0.043)

(0.068)

(0.07)

-0.007***

-0.009***

-0.026***

-0.026***

(0.001)

(0.001)

(0.002)

(0.002)

-0.001

(0.003)

0.051***

0.052***

0.167***

0.162***

(0.002)

(0.002)

(0.007)

(0.007)

-0.003

0.002

(0.002)

(0.004)

0.021***

0.020***

-0.006

-0.008*

(0.003)

(0.003)

(0.005)

(0.005)

-0.002

LCON,t-1*NPpoorCON,t
SharpeRE,t

-0.008***

(0.002)

LBUS,t-1*NPpoorBUS,t
LCON,t-1 (cross-sector)

-0.006

(0.002)

(0.004)

0.002***

0.002***

0.003***

0.003***

(0.000)

(0.000)

(0.0001)

(0.0001)

0.000**
SharpeRE,t* NPport t

Gt-1

-0.006

-0.040***

-0.042***

(0.004)

(0.004)

(0.01)

(0.01)

0.001
-0.009***

-0.011***

(0.002)

(0.002)

0.159***

URBAN
0.144***

(0.02)

(0.016)

(0.016)

-0.061

-0.027

0.114***

0.065*

(0.046)

(0.048)

(0.036)

(0.037)

0.011***

0.012***

0.015***

0.013***

(0.001)

(0.001)

(0.001)

(0.001)

0.000

-0.003**

(0.002)

(0.002)

-0.102***

-0.104***

-0.084***

-0.082***

(0.002)

(0.002)

(0.002)

(0.002)

0.006***

LBUS,t-1*NPpoorBUS,t

-0.005**

(0.002)

(0.002)

0.009***

0.009***

0.012***

0.010***

(0.003)

(0.003)

(0.002)

(0.002)

0.007***

LCON,t-1*NPpoorCON,t
SharpeBUS,t

(0.032)

-0.012***

(0.02)

LRE,t-1*NPpoorRE,t

LCON,t-1 (cross-sector)

0.024

(0.016)

constant
(0.001)
(0.001)
Panel B: Dependent Variable Net Change in Business Lending
RURAL
0.245***
0.266***
NLCRE,t

LBUS,t-1 (same-sector)

(0.0003)

-0.003

-0.010***

LRE,t-1 (cross-sector)

0.001***

(0.0001)

Gt-1* NPport t

NLCCON,t

0.002

(0.002)

(0.002)

0.007***

0.007***

0.007***

0.007***

(0.0002)

(0.0002)

(0.0004)

(0.0004)

0.000
SharpeBUS,t* NPport t

Gt-1

0.004***

(0.001)

(0.001)

0.019***

0.021***

0.028***

0.025***

(0.005)

(0.005)

(0.005)

(0.005)

-0.014

Gt-1* NPport t
Constant

URBAN
1.174***

(0.016)

LRE,t-1*NPpoorRE,t
LBUS,t-1 (cross-sector)

1.212***

0.000

(0.018)

(0.017)

0.002**

0.001

0.000

0.001

(0.001)

(0.001)

(0.001)

(0.001)

30

Panel C: Dependent Variable Net Change in Consumer Lending
RURAL
0.075***
0.070***
0.104***
NLCRE,t
NLCBUS,t
LRE,t-1 (cross-sector)

(0.008)

(0.007)

(0.025)

(0.024)

-0.012

-0.031***

0.003

-0.020*

(0.008)

(0.008)

(0.011)

(0.011)

-0.005***

-0.006***

-0.005***

-0.006***

(0.0004)

(0.0005)

(0.001)

(0.001)

0.000

LRE,t-1*NPpoorRE,t
LBUS,t-1 (cross-sector)

(0.001)

0.013***

0.012***

0.009***

0.007***

(0.001)

(0.001)

(0.003)

(0.003)

0.002**

-0.003**

(0.001)

(0.001)

-0.033***

-0.030***

-0.026***

-0.024***

(0.001)

(0.001)

(0.001)

(0.001)

-0.008***

LCON,t-1*NPpoorCON,t
SharpeCON,t

-0.006***

(0.001)

LBUS,t-1*NPpoorBUS,t
LCON,t-1 (same-sector)

-0.011***

(0.001)

(0.001)

0.002***

0.002***

0.003***

0.003***

(0.000)

(0.000)

(0.0001)

(0.0001)

-0.0004***
SharpeCON,t* NPport t

Gt-1

0.001**

(0.0002)

(0.0003)

0.001

0.000

0.002

-0.004

(0.002)

(0.002)

(0.003)

(0.004)

-0.001

Gt-1* NPport t
Constant

URBAN
0.056**

0.028***

(0.007)

(0.011)

0.001**

0.001***

0.000

0.001***

(0.0003)

(0.0003)

(0.001)

(0.001)

*All regressions include a constant, fixed effects for bank entity, and controls for quarterly effects. ***signifies statistical
significance at the .01 level, ** at the .05 level and * at the .10 level. The number of observations in the rural regression is
120,323; the number of observations in urban regressions is 69,013. The within R2s vary from negative to .034. This is not
surprising as the 2SLS or instrumental variables (IV) regression will not try to maximize the R2s as OLS does. Recall that
an OLS regression will maximize R2 without taking into account the endogeneity of the included NLC, and will result in
many negative estimated coefficients on NLC. In contrast, we estimate the model accounting for the endogeneity and
resulting in many positive estimated coefficients on the included NLC. For 2SLS and IV the R2 is calculated with fitted
values calculated using the estimated coefficient and the original data. We know that the values that maximize the R2
calculated this way would be the OLS coefficients, but we clearly do not want those, we want the estimated coefficients
accounting for the endogeneity. Hence it is not surprising that the calculated R2s may be negative.

31

Table 4: Estimation for Early and Late time periods*
Panel A: Dependent Variable Net Change in Real Estate Lending
Variable:
Early
Late
Early
RURAL
URBAN
0.215***
0.268***
0.664***
NLCBUS,t

Late
1.557***

(0.02)

(0.023)

(0.066)

(0.147)

0.187***

0.163***

0.091

-0.171

(0.047)

(0.066)

(0.061)

(0.135)

-0.048***

-0.041***

-0.076***

-0.043***

(0.002)

(0.002)

(0.003)

(0.004)

0.070***

0.062***

0.181***

0.230***

(0.005)

(0.005)

(0.012)

(0.019)

0.027***

0.034***

0.008

-0.032***

(0.005)

(0.006)

(0.007)

(0.01)

0.002***

0.002***

0.004***

0.003***

SharpeRE,t

(0.0001)

(0.0001)

(0.0001)

(0.0002)

Gt-1

0.018***

-0.024***

0.007

-0.066***

(0.008)

(0.008)

(0.015)

(0.019)

NLCCON,t
LRE,t-1 (same-sector)
LBUS,t-1 (cross-sector)
LCON,t-1 (cross-sector)

Panel B: Dependent Variable Net Change in Business Lending
Variable:
Early
Late
Early
RURAL
0.237***
0.228***
0.057***
NLCRE,t

Late
URBAN
0.118***

(0.029)

(0.026)

(0.023)

(0.022)

0.315***

-0.022***

0.171***

0.090

(0.055)

(0.074)

(0.039)

(0.059)

0.007**

0.014***

0.009***

0.009***

(0.003)

(0.003)

(0.003)

(0.002)

-0.175***

-0.164***

-0.152***

-0.113***

(0.003)

(0.003)

(0.004)

(0.004)

0.052***

0.019***

0.028***

0.010**

(0.006)

(0.007)

(0.004)

(0.004)

0.013***

0.006***

0.012***

0.006***

SharpeBUS,t

(0.0003)

(0.0002)

(0.0006)

(0.0005)

Gt-1

0.050***

0.043***

0.037***

0.024***

(0.01)

(0.008)

(0.01)

(0.009)

NLCCON,t
LRE,t-1 (cross-sector)
LBUS,t-1 (same-sector)
LCON,t-1 (cross-sector)

Panel C: Dependent Variable Net Change in Consumer Lending
Early
Late
Early
RURAL
0.054***
0.109***
0.093***
NLCRE,t
NLCBUS,t
LRE,t-1 (cross-sector)
LBUS,t-1 (cross-sector)
LCON,t-1 (same-sector)
SharpeCON,t

Late
URBAN
0.276***

(0.01)

(0.01)

(0.029)

(0.044)

0.004

-0.016*

0.062***

-0.006

(0.013)

(0.01)

(0.017)

(0.014)

0.002**

-0.009***

0.005***

-0.007***

(0.001)

(0.001)

(0.002)

(0.001)

0.020***

0.026***

0.021***

0.031***

(0.002)

(0.002)

(0.006)

(0.006)

-0.062***

-0.062***

-0.051***

-0.033***

(0.002)

(0.002)

(0.002)

(0.002)

0.002***

0.001***

0.004***

0.002***

(0.0001)

(0.0001)

(0.0001)

(0.0001)

0.014***

-0.005*

0.004

-0.007

Gt-1
(0.004)
(0.003)
(0.007)
(0.006)
*Standard errors are in parentheses below the coefficient estimates with * signifying different from zero at the 10% level,
** different from zero at the 5% level and *** as different from zero at the 1% level. The early period covers 1990, quarter
1 through 1996, quarter 2. The later period covers 1996, quarter 2 through 2002, quarter 4. All regressions include a
constant, fixed effects for bank entity, and controls for quarter effects. The number of observations in the early rural
regressions are 59,165 and in the later rural regressions 61,158; for urban regressions the number of observations is 36,843
for the early period and 32,170 for the later period. The within R2s vary from negative to .06.

32

Table 5: Banks in Multibank Holding Companies Only
Panel A: Dependent Variable Net Change in Real Estate Lending
0.5023***

URBAN
0.9313***

(0.057)

(0.11)

0.0457

0.3106***

(0.082)

(0.1)

-0.0364***

-0.0414***

(0.003)

(0.005)

0.1011***

0.2010***

(0.01)

(0.017)

-0.0023

-0.0022

(0.008)

(0.008)

0.0019

0.0033***

SharpeRE,t

(0.0001)

(0.0002)

Gt-1

-0.0250***

-0.0634***

(0.016)

(0.023)

.003

-.001***

(.002)

(.004)

RURAL
NLCBUS,t
NLCCON,t
LRE,t-1 (same-sector)
LBUS,t-1 (cross-sector)
LCON,t-1 (cross-sector)

constant

Panel B: Dependent Variable Net Change in Business Lending
URBAN
RURAL
0.2037***
0.1253***
NLCRE,t
(0.043)

(0.033)

0.0170

-0.0494

(0.071)

(0.059)

0.0098***

0.0126***

(0.003)

(0.003)

-0.1288***

-0.1267***

(0.005)

(0.006)

0.0181***

0.0124***

(0.007)

(0.005)

0.0080***

0.0091***

SharpeBUS,t

(0.0004)

(0.0008)

Gt-1

0.0224*

0.0017

(0.013)

(0.013)

.004*

.007***

(.002)

(.002)

NLCCON,t
LRE,t-1 (cross-sector)
LBUS,t-1 (same-sector)
LCON,t-1 (cross-sector)

constant

Panel C: Dependent Variable Net Change in Consumer Lending
URBAN
RURAL
0.0993***
-0.1675***
NLCRE,t
(0.025)

(0.05)

0.0098

0.0850***

(0.022)

(0.026)

-0.0029*

0.0030

(0.002)

(0.002)

0.0171***

-0.0227***

(0.004)

(0.008)

-0.0504***

-0.0215***

(0.003)

(0.003)

0.0031***

0.0042***

SharpeCON,t

(0.0001)

(0.0002)

Gt-1

-0.0168**

0.0203**

(0.007)

(0.01)

.0002

-.003*

NLCBUS,t
LRE,t-1 (cross-sector)
LBUS,t-1 (cross-sector)
LCON,t-1 (same-sector)

constant
(.001)
(.002)
*Standard errors are in parentheses below the coefficient estimates with * signifying different from zero at the 10% level,
** different from zero at the 5% level and *** as different from zero at the 1% level. All regressions include a constant,
fixed effects for bank entity, and controls for quarter effects. The number of observations in the rural regressions is 19,618,
the number in the urban regressions is 14,650. The within R2s vary from negative to .03.

33

Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
Outsourcing Business Services and the Role of Central Administrative Offices
Yukako Ono

WP-02-01

Strategic Responses to Regulatory Threat in the Credit Card Market*
Victor Stango

WP-02-02

The Optimal Mix of Taxes on Money, Consumption and Income
Fiorella De Fiore and Pedro Teles

WP-02-03

Expectation Traps and Monetary Policy
Stefania Albanesi, V. V. Chari and Lawrence J. Christiano

WP-02-04

Monetary Policy in a Financial Crisis
Lawrence J. Christiano, Christopher Gust and Jorge Roldos

WP-02-05

Regulatory Incentives and Consolidation: The Case of Commercial Bank Mergers
and the Community Reinvestment Act
Raphael Bostic, Hamid Mehran, Anna Paulson and Marc Saidenberg

WP-02-06

Technological Progress and the Geographic Expansion of the Banking Industry
Allen N. Berger and Robert DeYoung

WP-02-07

Choosing the Right Parents: Changes in the Intergenerational Transmission
of Inequality  Between 1980 and the Early 1990s
David I. Levine and Bhashkar Mazumder

WP-02-08

The Immediacy Implications of Exchange Organization
James T. Moser

WP-02-09

Maternal Employment and Overweight Children
Patricia M. Anderson, Kristin F. Butcher and Phillip B. Levine

WP-02-10

The Costs and Benefits of Moral Suasion: Evidence from the Rescue of
Long-Term Capital Management
Craig Furfine

WP-02-11

On the Cyclical Behavior of Employment, Unemployment and Labor Force Participation
Marcelo Veracierto

WP-02-12

Do Safeguard Tariffs and Antidumping Duties Open or Close Technology Gaps?
Meredith A. Crowley

WP-02-13

Technology Shocks Matter
Jonas D. M. Fisher

WP-02-14

Money as a Mechanism in a Bewley Economy
Edward J. Green and Ruilin Zhou

WP-02-15

1

Working Paper Series (continued)
Optimal Fiscal and Monetary Policy: Equivalence Results
Isabel Correia, Juan Pablo Nicolini and Pedro Teles

WP-02-16

Real Exchange Rate Fluctuations and the Dynamics of Retail Trade Industries
on the U.S.-Canada Border
Jeffrey R. Campbell and Beverly Lapham

WP-02-17

Bank Procyclicality, Credit Crunches, and Asymmetric Monetary Policy Effects:
A Unifying Model
Robert R. Bliss and George G. Kaufman

WP-02-18

Location of Headquarter Growth During the 90s
Thomas H. Klier

WP-02-19

The Value of Banking Relationships During a Financial Crisis:
Evidence from Failures of Japanese Banks
Elijah Brewer III, Hesna Genay, William Curt Hunter and George G. Kaufman

WP-02-20

On the Distribution and Dynamics of Health Costs
Eric French and John Bailey Jones

WP-02-21

The Effects of Progressive Taxation on Labor Supply when Hours and Wages are
Jointly Determined
Daniel Aaronson and Eric French

WP-02-22

Inter-industry Contagion and the Competitive Effects of Financial Distress Announcements:
Evidence from Commercial Banks and Life Insurance Companies
Elijah Brewer III and William E. Jackson III

WP-02-23

State-Contingent Bank Regulation With Unobserved Action and
Unobserved Characteristics
David A. Marshall and Edward Simpson Prescott

WP-02-24

Local Market Consolidation and Bank Productive Efficiency
Douglas D. Evanoff and Evren Örs

WP-02-25

Life-Cycle Dynamics in Industrial Sectors. The Role of Banking Market Structure
Nicola Cetorelli

WP-02-26

Private School Location and Neighborhood Characteristics
Lisa Barrow

WP-02-27

Teachers and Student Achievement in the Chicago Public High Schools
Daniel Aaronson, Lisa Barrow and William Sander

WP-02-28

The Crime of 1873: Back to the Scene
François R. Velde

WP-02-29

Trade Structure, Industrial Structure, and International Business Cycles
Marianne Baxter and Michael A. Kouparitsas

WP-02-30

Estimating the Returns to Community College Schooling for Displaced Workers
Louis Jacobson, Robert LaLonde and Daniel G. Sullivan

WP-02-31

2

Working Paper Series (continued)
A Proposal for Efficiently Resolving Out-of-the-Money Swap Positions
at Large Insolvent Banks
George G. Kaufman

WP-03-01

Depositor Liquidity and Loss-Sharing in Bank Failure Resolutions
George G. Kaufman

WP-03-02

Subordinated Debt and Prompt Corrective Regulatory Action
Douglas D. Evanoff and Larry D. Wall

WP-03-03

When is Inter-Transaction Time Informative?
Craig Furfine

WP-03-04

Tenure Choice with Location Selection: The Case of Hispanic Neighborhoods
in Chicago
Maude Toussaint-Comeau and Sherrie L.W. Rhine

WP-03-05

Distinguishing Limited Commitment from Moral Hazard in Models of
Growth with Inequality*
Anna L. Paulson and Robert Townsend

WP-03-06

Resolving Large Complex Financial Organizations
Robert R. Bliss

WP-03-07

The Case of the Missing Productivity Growth:
Or, Does information technology explain why productivity accelerated in the United States
but not the United Kingdom?
Susanto Basu, John G. Fernald, Nicholas Oulton and Sylaja Srinivasan

WP-03-08

Inside-Outside Money Competition
Ramon Marimon, Juan Pablo Nicolini and Pedro Teles

WP-03-09

The Importance of Check-Cashing Businesses to the Unbanked: Racial/Ethnic Differences
William H. Greene, Sherrie L.W. Rhine and Maude Toussaint-Comeau

WP-03-10

A Firm’s First Year
Jaap H. Abbring and Jeffrey R. Campbell

WP-03-11

Market Size Matters
Jeffrey R. Campbell and Hugo A. Hopenhayn

WP-03-12

The Cost of Business Cycles under Endogenous Growth
Gadi Barlevy

WP-03-13

The Past, Present, and Probable Future for Community Banks
Robert DeYoung, William C. Hunter and Gregory F. Udell

WP-03-14

Measuring Productivity Growth in Asia: Do Market Imperfections Matter?
John Fernald and Brent Neiman

WP-03-15

Revised Estimates of Intergenerational Income Mobility in the United States
Bhashkar Mazumder

WP-03-16

3

Working Paper Series (continued)
Product Market Evidence on the Employment Effects of the Minimum Wage
Daniel Aaronson and Eric French

WP-03-17

Estimating Models of On-the-Job Search using Record Statistics
Gadi Barlevy

WP-03-18

Banking Market Conditions and Deposit Interest Rates
Richard J. Rosen

WP-03-19

Creating a National State Rainy Day Fund: A Modest Proposal to Improve Future
State Fiscal Performance
Richard Mattoon

WP-03-20

Managerial Incentive and Financial Contagion
Sujit Chakravorti, Anna Llyina and Subir Lall

WP-03-21

Women and the Phillips Curve: Do Women’s and Men’s Labor Market Outcomes
Differentially Affect Real Wage Growth and Inflation?
Katharine Anderson, Lisa Barrow and Kristin F. Butcher

WP-03-22

Evaluating the Calvo Model of Sticky Prices
Martin Eichenbaum and Jonas D.M. Fisher

WP-03-23

The Growing Importance of Family and Community: An Analysis of Changes in the
Sibling Correlation in Earnings
Bhashkar Mazumder and David I. Levine

WP-03-24

Should We Teach Old Dogs New Tricks? The Impact of Community College Retraining
on Older Displaced Workers
Louis Jacobson, Robert J. LaLonde and Daniel Sullivan

WP-03-25

Trade Deflection and Trade Depression
Chad P. Brown and Meredith A. Crowley

WP-03-26

China and Emerging Asia: Comrades or Competitors?
Alan G. Ahearne, John G. Fernald, Prakash Loungani and John W. Schindler

WP-03-27

International Business Cycles Under Fixed and Flexible Exchange Rate Regimes
Michael A. Kouparitsas

WP-03-28

Firing Costs and Business Cycle Fluctuations
Marcelo Veracierto

WP-03-29

Spatial Organization of Firms
Yukako Ono

WP-03-30

Government Equity and Money: John Law’s System in 1720 France
François R. Velde

WP-03-31

Deregulation and the Relationship Between Bank CEO
Compensation and Risk-Taking
Elijah Brewer III, William Curt Hunter and William E. Jackson III

WP-03-32

4

Working Paper Series (continued)
Compatibility and Pricing with Indirect Network Effects: Evidence from ATMs
Christopher R. Knittel and Victor Stango

WP-03-33

Self-Employment as an Alternative to Unemployment
Ellen R. Rissman

WP-03-34

Where the Headquarters are – Evidence from Large Public Companies 1990-2000
Tyler Diacon and Thomas H. Klier

WP-03-35

Standing Facilities and Interbank Borrowing: Evidence from the Federal Reserve’s
New Discount Window
Craig Furfine

WP-04-01

Netting, Financial Contracts, and Banks: The Economic Implications
William J. Bergman, Robert R. Bliss, Christian A. Johnson and George G. Kaufman

WP-04-02

Real Effects of Bank Competition
Nicola Cetorelli

WP-04-03

Finance as a Barrier To Entry: Bank Competition and Industry Structure in
Local U.S. Markets?
Nicola Cetorelli and Philip E. Strahan

WP-04-04

The Dynamics of Work and Debt
Jeffrey R. Campbell and Zvi Hercowitz

WP-04-05

Fiscal Policy in the Aftermath of 9/11
Jonas Fisher and Martin Eichenbaum

WP-04-06

Merger Momentum and Investor Sentiment: The Stock Market Reaction
To Merger Announcements
Richard J. Rosen

WP-04-07

Earnings Inequality and the Business Cycle
Gadi Barlevy and Daniel Tsiddon

WP-04-08

Platform Competition in Two-Sided Markets: The Case of Payment Networks
Sujit Chakravorti and Roberto Roson

WP-04-09

Nominal Debt as a Burden on Monetary Policy
Javier Díaz-Giménez, Giorgia Giovannetti, Ramon Marimon, and Pedro Teles

WP-04-10

On the Timing of Innovation in Stochastic Schumpeterian Growth Models
Gadi Barlevy

WP-04-11

Policy Externalities: How US Antidumping Affects Japanese Exports to the EU
Chad P. Bown and Meredith A. Crowley

WP-04-12

Sibling Similarities, Differences and Economic Inequality
Bhashkar Mazumder

WP-04-13

Determinants of Business Cycle Comovement: A Robust Analysis
Marianne Baxter and Michael A. Kouparitsas

WP-04-14

5

Working Paper Series (continued)
The Occupational Assimilation of Hispanics in the U.S.: Evidence from Panel Data
Maude Toussaint-Comeau

WP-04-15

Reading, Writing, and Raisinets1: Are School Finances Contributing to Children’s Obesity?
Patricia M. Anderson and Kristin F. Butcher

WP-04-16

Learning by Observing: Information Spillovers in the Execution and Valuation
of Commercial Bank M&As
Gayle DeLong and Robert DeYoung

WP-04-17

Prospects for Immigrant-Native Wealth Assimilation:
Evidence from Financial Market Participation
Una Okonkwo Osili and Anna Paulson

WP-04-18

Institutional Quality and Financial Market Development:
Evidence from International Migrants in the U.S.
Una Okonkwo Osili and Anna Paulson

WP-04-19

Are Technology Improvements Contractionary?
Susanto Basu, John Fernald and Miles Kimball

WP-04-20

The Minimum Wage, Restaurant Prices and Labor Market Structure
Daniel Aaronson, Eric French and James MacDonald

WP-04-21

Betcha can’t acquire just one: merger programs and compensation
Richard J. Rosen

WP-04-22

Not Working: Demographic Changes, Policy Changes,
and the Distribution of Weeks (Not) Worked
Lisa Barrow and Kristin F. Butcher

WP-04-23

The Role of Collateralized Household Debt in Macroeconomic Stabilization
Jeffrey R. Campbell and Zvi Hercowitz

WP-04-24

Advertising and Pricing at Multiple-Output Firms: Evidence from U.S. Thrift Institutions
Robert DeYoung and Evren Örs

WP-04-25

Monetary Policy with State Contingent Interest Rates
Bernardino Adão, Isabel Correia and Pedro Teles

WP-04-26

Comparing location decisions of domestic and foreign auto supplier plants
Thomas Klier, Paul Ma and Daniel P. McMillen

WP-04-27

China’s export growth and US trade policy
Chad P. Bown and Meredith A. Crowley

WP-04-28

Where do manufacturing firms locate their Headquarters?
J. Vernon Henderson and Yukako Ono

WP-04-29

Monetary Policy with Single Instrument Feedback Rules
Bernardino Adão, Isabel Correia and Pedro Teles

WP-04-30

6

Working Paper Series (continued)
Firm-Specific Capital, Nominal Rigidities and the Business Cycle
David Altig, Lawrence J. Christiano, Martin Eichenbaum and Jesper Linde

WP-05-01

Do Returns to Schooling Differ by Race and Ethnicity?
Lisa Barrow and Cecilia Elena Rouse

WP-05-02

Derivatives and Systemic Risk: Netting, Collateral, and Closeout
Robert R. Bliss and George G. Kaufman

WP-05-03

Risk Overhang and Loan Portfolio Decisions
Robert DeYoung, Anne Gron and Andrew Winton

WP-05-04

7