SIGNALLING PROCESS AND SELF-SELECTION MECHANISM
IN ENTREPRENEURIAL FINANCE
Working Paper No. 97
May 2008
Liang Han, Stuart Fraser and David J Storey
Warwick Business School’s Small and Medium Sized Enterprise Centre Working
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1
Signalling Process and Self-Selection Mechanism in Entrepreneurial Finance
Liang Han - Hull University Business School *
Stuart Fraser - Warwick Business School
David J. Storey - Warwick Business School
Abstract
This paper develops Bester’s (1985) model by incorporating a signalling process into the
design of an incentive-compatible menu of contracts which works as a self-selection
mechanism. It then tests this Signalling and Self-Selection Model, using the 1998 U.S. Survey
of Small Business Finances. It reports for the first time that high type entrepreneurs are
more likely to pledge collateral and entrepreneurs who transfer good signals enjoy better
contracts than those transferring bad signals. This implies that this model sheds more light
on entrepreneurial debt finance than either the sorting-by-observed-risk or the sorting-byprivate information paradigm.
JEL Classification: D81, D82, G1
Keywords:
*
Signalling, Self-Selection, Collateral,
Contracts
Corresponding author: L.Han@hull.ac.uk
2
Asymmetric information is central to understanding the relationship between banks and small
businesses. The asymmetry occurs because bank lenders are generally assumed to have less good
information about the individual small business than the borrower. Two strategies, both relating
to collateral, can address this issue (Berger and Udell, 1990). The first is for the lender to require
the borrower to provide collateral, with that collateral passing to the lender in the event of a
default.
This
is
called
‘sorting-by-observed-risk
(SBOR)’
by
which
collateral
is
determined/required by the demand side, i.e. lender. The second is to enable good borrowers to
reliably reveal themselves, and by rewarding them with a ‘good’ contract. One reliable signal may
be the borrower offering collateral. This is called ‘sorting-by-private-information (SBPI)’ by
which collateral is determined/offered by supply side, i.e. borrower. Berger and Udell’s empirical
work supported the SBOR paradigm, implying that observably risky small firms are required to
pledge collateral.
Nevertheless an earlier theoretical paper by Bester (1985), had elegantly demonstrated that the
willingness to pledge collateral by good borrowers could be taken as a reliable signal of borrower
quality by an imperfectly informed lender. Bester’s model demonstrated that SBPI was certainly
possible. This paper develops the Bester theory in a number of ways, highlighting the role that
can be played by collateral in both signalling process † and self-selection mechanism. It proposes
that high-type or ‘good’ entrepreneurs who have less risky projects and higher project returns
pledge more collateral and obtain lower interest rates than low-type or ‘bad’ entrepreneurs who
†
In this paper, ‘signalling’ means the process by which a lender makes lending decision by collecting information
from ‘observable signals’ transferred by a borrower. In contrast, Bester (1985) refers ‘signalling’ as a mechanism by
which a borrower discloses her quality to a lender by pledging collateral on loans.
3
have riskier projects and lower project returns. Second, it defines the conditions under which
entrepreneurs who transfer good signals enjoy lower interest rates/collateral compared with
those with bad signals. Thirdly it shows that not all entrepreneurs benefit from developing a
closer relationship with the bank, because those transferring bad signals may suffer higher
interest rates, even if they are of high-type. Finally it considers the nature of the signals accepted
as legitimate by the bank. These include the nature and duration of the relationship between the
lender and borrower; they also include a distinction between signals about the owner of the
business and those relating to measures of business.
The model differs from previous theoretical models in several important respects. For example,
the model of Stiglitz and Weiss (1981) depicts the problem of information asymmetry as being
where the bank does not know the probability of success and the project return if it is
successful ‡ . Our model instead assumes the bank does not know exactly the type of the
entrepreneur, but does know the project returns of different entrepreneurs. We assume that only
by observing the signals transferred by the entrepreneur can the bank estimate a probability of
the entrepreneur being either a high-type or a low-type.
‡
Because of these different assumptions, credit rationing occurs in Stiglitz and Weiss (1981) and Jaffee and Russell
(1984) but it does not occur in our model. This is because of our assumption that both the borrower and lender
know the expected default probability of the borrower. Therefore, both the entrepreneur and the bank act on the
default probability as if it were a certain value. Thus, there is no moral hazard; the default risk is built into the
interest rate; and credit rationing does not occur. Our model also differs from that of Jaffee and Russell (1976) who
assume honest and dishonest borrowers with different default propensities, which are known to themselves only,
while the lender must act on the aggregate average default propensity. As a result, the lender treats each borrower as
if they had the average propensity. There is thus a necessary asymmetry between the borrower and lender, from
which an adverse selection problem arises, and credit rationing results (Jaffee and Russell, 1984).
4
Given these modelling assumptions the current paper uses the 1998 U.S. Survey of Small
Business Finances to compare the explanatory power of the SBOR and SBPI paradigms and the
current ‘Signalling and Self-Selection (SASS)’ model. In contrast with Berger and Udell (1990),
our model provides more insights than the pure SBOR and SBPI paradigm. It finds that riskier
entrepreneurs are less likely to pledge collateral and that entrepreneurs with good signals enjoy
more favourable debt contracts than those with bad signals. It also finds that relationship lending
reduces the interest rates significantly. This result contrasts with the earlier findings of Petersen
and Rajan (1994). The paper is structured as follows. Section 1 sets up the model and solves for
the equilibrium. Section 2 addresses some empirical implications and hypotheses derived from
the model. Section 3 describes the data and variables used in this paper. Section 4 conducts
econometric regressions and tests the hypotheses. Finally, Section 5 summarises and concludes.
1. THE MODEL
1.1 Setting-up
The model describes an economy in which an entrepreneur undertakes a one-period project,
which requires an exogenous industry-specific investment § , K, by raising funds, K, from a bank **
§
We follow Bester (1987), but not Evans and Jovanovic (1989) on this point. This is because with asymmetric
information, fixed investment size precludes signalling of entrepreneur’s type by the level of investment. In Evans
and Jovanovic (1989), abler entrepreneurs would have higher optimal capital demands to maximize their yield as the
“abler entrepreneur has a higher total product and a higher marginal product of capital at all levels of capital”
(p.811).
**
In practice, investment may come from both personal wealth of the entrepreneur and the bank. Theoretically,
however, if the output is public knowledge without private information, the debt-equity choice is irrelevant (Webb,
5
that offers a menu of contracts for different types of entrepreneurs. The entrepreneur is
endowed with collateral W and this is her only personal wealth. The bank’s offering depends
upon the signals he †† observes since the entrepreneurial type is private information known to the
entrepreneur only. Both the bank and the entrepreneur are risk neutral and the risk-free interest
rate is normalised to zero.
With a probability of p, the project undertaken succeeds with a return of (1+θ) K, which is a
function of the entrepreneurial ability (θ) and investment (K). Otherwise, with a probability of (1p), the project fails and the entrepreneur gets a return of zero. For simplicity, the project state
and return is observable without any cost and the entrepreneur repays when the project is
successful and defaults when it fails. There are only two types of entrepreneurs, high-type ( θ H )
and low-type ( θ L ), where θ = {θ L ,θ H } ∈ (0,1) and θ is the entrepreneur’s private information.
The probability of success, p, equals the entrepreneurial ability of the entrepreneur who
undertakes the project, meaning that the probability of success is also either high ( p H = θ H ) or
low ( p L = θ L ). Thus the project return ‡‡ can be written as
⎧(1 + θ ) K
return = ⎨
⎩ 0
w. p. θ
………… (1)
w. p. 1 − θ
1991). Thus such a setup may induce extreme finance methods, fully self-finance or fully external financing (de
Meza and Webb, 1987).
††
For clarity of explanation, the bank will be male and the borrower female.
‡‡
An important implication of the project return function is that when the project succeeds, both low-type and
high-type entrepreneurs have a positive net payoff. This is the motivation for both types of entrepreneurs to
undertake the project. In other words, the project has a positive net present value in a success scenario for both
high-type and low-type entrepreneurs.
6
where θ = {θ L ,θ H } . Unlike returns of riskier borrowers defined by Bester (1985, 1987) and
Stiglitz and Weiss (1981), the returns of low type borrowers are not a mean preserving spread of
the returns of high type borrowers. Instead, the project return is a function of probability, θ, and
zero otherwise, so that both the expected return and the distribution vary with the borrower type
θ. Thus, the returns of high type entrepreneurs first order stochastically dominate the returns low
type entrepreneurs §§ .
The financing contract is standard and defined by two factors, interest rate r and collateral C
which, for simplicity, is assumed to be unconstrained by the entrepreneur’s initial wealth. The
utility function of the entrepreneur is pecuniary-based and the utility is entirely determined by the
amount of wealth at the end of the period. Thus, when the project succeeds, the entrepreneur
has a utility U S which equals her initial assets plus project return and minus the repayment;
whereas, if the project fails, her utility U F is her initial assets minus the collateral transferred to
the bank because of default. So, U S , U F and her expected utility EU, respectively are
U S = W + (1 + θ ) K − (1 + r ) K = W + (θ − r ) K w.p. θ………(2)
U F =W −C
w.p. 1-θ…………….(3)
and
§§
Therefore, entrepreneurs are categorised as low-type and high-type, instead of riskier and safer ones. This is
because the latter categorisation usually involves second order stochastic dominance.
7
EU = θU S + (1 − θ )U F = θ 2 K − rθK + W − (1 − θ )C …………(4).
1.2 Signalling and the Bank’s Offer
The prior distribution of borrower’s type estimated by the bank is either high ( θ H ) or low ( θ L )
with equal probability *** . The conditional probability of the signal, which is either good ( s ) or
bad ( s ) observed by the bank, is Pr( s | θ h ) = Pr( s | θ l ) = α , and Pr( s | θ l ) = Pr( s | θ h ) = 1 − α ,
where α ≥ 0.5 and it measures the severity of information asymmetry between the entrepreneur
and the bank. Thus, the posterior distribution of the entrepreneur’s type, given this signal, is
Pr(θ = θ h | s = s) = Pr(θ = θ L | s = s ) =
0.5α
= α ………….(5),
0.5α + 0.5(1 − α )
and
Pr(θ = θ l | s = s ) = Pr(θ = θ h | s = s ) = 1 − α ………………(6),
meaning that when the bank observes a good (bad) signal, he supposes that the entrepreneur has
a probability of α to be a high-type (low-type) entrepreneur and a probability of (1-α) to be a
low-type (high-type) entrepreneur. This is referred to as signalling process and observable signals
can be, empirically, business performance, demographics of entrepreneur and so on.
***
Here we assume either (a) the bank is ignorant of the respective proportions of high-type borrowers and low-type
borrowers in the population; or (b) there is an equal number of high-type borrowers and low-type borrowers in the
population.
8
It is assumed that the bank offers a menu of contracts: ΓH (rH , C H ) for high-type entrepreneurs
and ΓL (rL , C L ) for low-type entrepreneurs. When the project succeeds, the entrepreneur repays
(1+r)K to the bank; when borrower defaults, the bank claims the ownership of C. Thus the
expected profit of the bank is
Eπ = α [θ H (1 + rH ) K + (1 − θ H )C H − K ] + (1 − α )[θ L (1 + rL ) K + (1 − θ L )C L − K ] ….(7),
when the bank observes a good signal ( s ) and the following one if he observes s
Eπ = (1 − α )[θ H (1 + rH ) K + (1 − θ H )C H − K ] + α [θ L (1 + rL ) K + (1 − θ L )C L − K ] ..(8)
1.3 Self-Selection Mechanism
The menu of contracts offered by the bank could work as a self-selection mechanism under the
condition that the menu satisfies the Individual Rationality (IR) and the Incentive Compatibility
(IC) condition. The IR condition requires that the expected utility of undertaking a risky action
of both lenders and borrowers is no less than their initial utility if not undertaking the action.
Specifically, the IR condition of the entrepreneur is
EU i (Γi ) = θ i K − riθ i K − (1 − θ i )C i ≥ W , where i = {L, H } …….(9);
2
and that of the bank requires that Eπ ≥ 0 , when s = s and Eπ ≥ 0 when s = s . The IC
condition requires that the menu of contracts makes each type of entrepreneur choose the right
9
type of contract intended for her; otherwise, she is worse off. The IC conditions could be
expressed as EU H (ΓH ) > EU H (ΓL ) for high-type entrepreneur and EU L (ΓL ) > EU L (ΓH ) for
low-type entrepreneur, therefore. The incentive-compatible menu of contracts works because the
marginal (dis)utility of interest rate and collateral differs between low-type and high-type
entrepreneurs, as shown in Figure 1. By manipulating the equations discussed so far, we have the
Proposition as follows
Figure 1: around here please.
Proposition The high-type entrepreneur chooses a contract with a lower interest rate and a
higher collateral requirement to maximise her expected utility at
max EU H ( ΓH ) = θ H K + W −
2
[1 − θ − (1 − α )θ L ]K
2
α
……..(10)
when she transfers a good signal to the bank and
max EU H ( ΓH ) = θ H
(1 − θ − αθ L ) K
………(11)
K +W −
1−α
2
2
when she transfers a bad signal to the bank. A low-type entrepreneur chooses a contract with a
higher interest rate and a lower collateral requirement to maximise her expected utility at
10
(1 − θ − αθ H ) K
………….(12)
max EU L ( ΓL ) = θ L K + W −
1−α
2
2
when she transfers a good signal to the bank and
max EU L ( ΓL ) = θ L K + W −
2
[1 − θ − (1 − α )θ H ]K
2
α
…………..(13)
when a bad signal is observed, where θ = αθ H + (1 − α )θ L and θ = (1 − α )θ H + αθ L .
Proof: See Appendix A.
2. EMPIRICAL IMPLICATIONS AND HYPOTHESES
Corollary 1 A large borrower, who borrows more from the bank, pays a lower interest rate and
pledges more collateral on loans.
Figure 2: around here please.
As Figure 2 shows, when K increases, the slope of the expected utility of the entrepreneur with
interest rate and collateral becomes flatter. Thus, it is predicted that an entrepreneur with a larger
amount of borrowing has an optimal contract with a lower interest rate and a larger amount of
collateral.
11
Corollary 2 The entrepreneur enjoys a lower interest rate and/or a lower collateral requirement
by transferring a good signal than bad signal.
When a good signal is observed, the bank’s posterior probability of the entrepreneur being of
high-type is α, where α ≥ 0.5 , suggesting that the bank supposes that the entrepreneur is more
likely to be of high-type and has a higher probability to repay. To break even, the bank can
charge a lower interest rate and/or lower collateral, holding other factors constant.
Corollary 3 Relationship lending reduces interest rates on loans when bank observes a good
signal and increases interest rates on loans when bank observes a bad signal.
The formal derivation of this corollary is shown in Appendix B, with an intuitive explanation
provided here. We assume the relationship between lender and borrower is a measure of
asymmetric information. The information problem can be alleviated by developing longer
relationships between the entrepreneur and the bank (Berger and Udell, 1995). To some extent,
Corollary 3 differs from previous empirical studies (e.g. Petersen and Rajan, 1994; Berger and
Udell, 1995) which did not distinguish signals. We assume entrepreneurial type is private
information and is unknown to the bank. The bank can only estimate the probability of the
entrepreneur being either high-type or low-type by observing the signals transferred from the
entrepreneur; so, the estimated probability depends on two factors: the signal and the severity of
information asymmetry. The good entrepreneur would therefore be expected to make positive
12
signals and expected to be rewarded, in the form of lower interest rates. To summarise, the
above theory development leads to five specific hypotheses, specified below. These are then
tested in section 4.
H1: High-type entrepreneurs are more likely to choose a contract with more collateral and lowtype entrepreneurs are more likely to choose a contract with less collateral (Proposition).
H2: The amount of collateral and interest rates are inversely associated. In other words, hightype entrepreneurs can enjoy lower interest rates by pledging more collateral (Proposition).
H3: Loan size is positively related to the amount of collateral and negatively related to interest
rate. In other words, the more the entrepreneur borrows the more collateral she pledges and the
lower is the interest rate charged (Corollary 1).
H4: Entrepreneurs who transfer good signals enjoy lower interest rates and/or lower collateral
(Corollary 2).
H5: Relationship lending reduces interest rates on loans when bank observes a good signal and it
increases interest rates on loans when bank observes a bad signal (Corollary 3).
The hypotheses, as shown, integrate the key implications from SBOR and SBPI which treat
signalling and self-selection mechanism as separate responses to the problem of information
asymmetry in entrepreneurial finance. The SASS model, however, combines the signalling
process and self-selection mechanism in financing entrepreneurial firms.
3. DATA AND VARIABLES
13
3.1 Data: 1998 U.S Survey of Small Business Finances
The empirical materials used in this paper to test the hypotheses specified in Section 2 are
derived from the 1998 U.S. Survey of Small Business Finances (SSBF98). The SSBF survey
collects information on the use of credit by small firms and creates a general-purpose database
on the finances of such firms. This survey was funded and conducted by the Federal Reserve and
Small Business Administration in the U.S, and it was previously conducted in 1987 and 1993,
respectively, with a target population of all for-profit, non-financial, non-farm, non-subsidiary
businesses with fewer than 500 employees. The dataset of the 1998 survey for public use
contains 3,561 sample firms, representing 5.3 million small businesses in the U.S. The 1998 SSBF
survey also provides detailed information about the most recent loans of 796 sample firms who
borrowed in the three years prior to the survey.
3.2 Variables
As theoretically modelled earlier, the key determinants of loan contract terms include (1)
observable signals transferred by borrowers, (2) borrower’s quality which is regarded as private
information, which a lender does not know or does not know exactly, and (3) the severity of the
problem of information asymmetries between lender and borrower.
Here, we represent the ‘observable signals’ by the characteristics of the business and
entrepreneur, controlling for the loan characteristics. Panel A (Table 1) presents the main
descriptive statistics of the characteristics of the business and entrepreneur, including all 3,561
14
sample firms. A ‘typical’ small firm in the U.S. is around 14 years old with 26 employees, family
owned and owner-managed by an entrepreneur of 51 years old who has 19 years experience in
business and management.
Table 1: around here please
Panel B (Table 1) reports the descriptive statistics of the characteristics of the most recent loans
borrowed by 796 sample firms. As shown, 63 per cent of most recent loans were collateralised
and the average size of loan was around $0.47 million, ranging from $100 to $24 million. Around
52 per cent of the loans had a value below $50,000 and 30% had a value greater than $150,000.
53 percent of the most recent loans borrowed by small businesses were in the form of either
capital lease or vehicle/equipment loans. Panel B also reports that banks were the primary lender
which provided 70% of all small business loans and the mean interest rate charged on loans was
9.04 percent, with two third of the loans carrying fixed interest rates.
Apart from the characteristics of the business, entrepreneur and loan which were derived from
the survey directly, we also collected information on industry and market level from other
sources, such as the profitability and risk of the industry from
COMPUSTAT,
the prime rate and
default spread in the month when the sample firms borrowed the loans from DataStream. The
objective of doing so is to examine how industry and market level factors influence small
business borrowing.
15
The second determinant is the private information, borrower’s quality. Borrower’s quality can be
measured by a Dun and Bradstreet (D&B) Score (Cavalluzzo et al. 2002), the variance of returns
to equity (Booth and Booth, 2006) or by cash management behaviour (Laitinen and Laitinen,
1998). Neither, however, are appropriate measures for the analysis of the effects of private
information on financing choices in our case because such information is publicly available and
so will underestimate the effects of information imperfections. Another possible danger of using
these variables directly to represent borrower’s quality, along with characteristics of the business
and entrepreneur, is endogeneity. This is because these risk variables may be endogenously
determined by the characteristic variables, such as credit history. To overcome the problems, we
therefore use instrumented D&B scores ††† to measure the risk levels of borrowers and controlled
for the samples which borrowed before the signals were observed. Thirdly, we measure the
severity of the information problem by the length of relationship with lender; this measure has
been widely used in the existing empirical literature (e.g. Berger and Udell, 1995; Petersen and
Rajan, 1994) and a review is available from Holland (1994).
Table 2 reports simple continuous (Panels A and B) and bivariate (Panel C) correlations on the
independent variables, respectively. Panel A reports the correlation matrix of the ‘observable
signals’, i.e. the characteristics of the business and entrepreneur, with all sample firms. By Panels
B and C, we examine the correlations of ‘observable signals’ of borrowers by controlling for the
†††
We estimate the instrumented D&B scores by conducting ordered logistic models on the business and
entrepreneur variables and their credit history. A continuous instrument was constructed (INST_DB2) and
calculated as a weighted average of the different risk levels (i.e., the expected risk level) where the weight is the
probability of a sample falling into a particular risk category, which is estimated from the ordered logistic model.
Details of the instrumentation process are available from the authors upon request.
16
loan characteristics, with 796 samples. Table 2 shows that none is above 0.75 for continuous
variables (Panels A and B) and apart from the high correlations between the mutually exclusive
loan size bands, all of others are under 0.40 (Panel C). Thus, multicollinearity problems are
minimised and giving justification for our following regression models.
Table 2: around here please
4. EMPIRICAL RESULTS
In this section, we conduct empirical analysis on the data from the 1998 U.S. Survey of Small
Business Finances to test the hypotheses derived from the theoretical modelling of sorting-bysignalling- and-self-selection (SBSS) paradigm. For comparison purpose, we also test the sortingby-observed-risk (SBOR) and sorting-by-private-information (SBPI) paradigms. In the following
sub-sections, we begin the analysis with univariate tests on the possible determinants of
collateralising a loan and then examine them by multivariate analysis. Finally, we investigate the
determination of the interest rates charged on small business loans.
4.1 Univariate Tests
Table 3 reports the results of univariate tests. Firstly, in terms of ‘observable signals’, or
characteristics of business and entrepreneur, borrowers which pledged collateral, on average,
were slightly older (C_FAGE), much larger in size measured by total number of employees
(TOTEMP), less likely to be owner-managed (OWNER_MANAGED) and more likely to have bad
17
credit history such as firm delinquency (FIRM_DELINQUENCT), than borrowers who did not
pledge collateral on loans. This suggests an important role played by observable signals according
to SBOR and SBSS. Moreover, those entrepreneurs who collateralised were also slightly older
(C_OAGE), more experienced (C_EXP), more likely to be well-educated (DEGREE) and less likely
to be ethnic-minority (MINOR). These results imply that collateral may not be entirely determined
by the demand side, or required by lenders from observably risky borrowers as predicted by
SBOR. This is because the results of univariate tests suggest that collateral suppliers, i.e.
borrowers, also strongly affect the collateralisation, such as larger firms who are supposed to be
less risky.
Table 3: around here please.
Secondly, Table 3 shows that there was little difference in terms of risk levels between borrowers
who collateralised and those who did not if the risk level was measured by Dun&BradStreet
Score (DB_SCORE). However, by comparing the instrumented risk measure (INST_DB2),
borrowers who collateralised were less risky than those who did not collateralise; and the
difference is statistically significant at a 5% level. This result crudely supports the prediction of
SBPI and SBSS paradigm where good borrowers are more likely to pledge collateral on loans.
Thirdly, Table 3 also suggests that collateralisation may be transaction motivated. For example,
larger loans, equipment loans and loans with longer maturity were more likely to be collateralised.
Furthermore, there is a trade-off relationship between collateralisation and interest rates, which is
18
inconsistent with the empirical findings of Berger and Udell (1990) who reported a positive
relationship.
Fundamentally, the univariate test results suggest that both signalling process and self-selection
may have strong impacts on the determination of loan contract terms. However, neither
provides a comprehensive prediction on loan contract determination by its own.
4.2 The Probability of Collateralisation
In this sub-section, we empirically examine the probability of a loan being collateralised
according to the predictions of SBOR, SBPI and SBSS, respectively. In the following analysis,
firstly, we use probit models to test SBOR and then conduct probit models with endogenous
covariates to examine the trade-off between collateral and interest rates coherently where interest
rates are endogenously determined. Secondly, we disentangle the borrower risk from the
transaction effects of loan, i.e. loan size, by conducting models with different measures of loan
size, such as natural log transformed loan size (model 1), loan size bands (model 2), and the
interaction terms between loan size and borrower’s risk (models 3 and 4). Thirdly, in the test of
SBOR, we control for the sample firms who borrowed AFTER the signals can be observed so
that lenders/borrowers can make the decision with all signals observable. In other words, such
borrowers borrowed after the end of their financial year. In the tests of SBPI and SBSS, we
control for the samples who borrowed BEFORE the end of their financial year and thus their
characteristics were literally not observable for banks before making the lending decision. Finally,
19
since the private information measure, i.e. instrumented D&B score is a generated regressor, we
adjust the standard errors in the regressions by bootstrapping approach.
Table 4 reports the results of probit models with restricted specifications and the dependent
variable modelled is the probability of a loan being collateralised, i.e. COLLATERAL=1. The results
reported here suggest that the likelihood of collateralisation is mainly determined by loan
characteristics and the observable signals of the borrower (models 1and 2). For example, larger
loans and vehicle/equipment loans are more likely to be collateralised. By including interaction
terms between loan size and borrower’s risk in the regressions, we find that the individual loan
size measures become statistically insignificant and the interaction terms have significant impacts
on the likelihood of collateralisation. Hence, this finding implies that borrower’s risk level is a
more important factor, than loan size, in determining the likelihood. If a riskier borrower
borrowed a larger amount of loan, the risk undertook by lenders is ‘doubled’ by both riskier
borrower and riskier loans and thus a greater likelihood of collateralisation is observed. The
results reported in Table 4 also suggest that borrowers who transferred ‘bad’ signals had a higher
probability of collateralising their loans. Indeed, borrowers in riskier industry or having judgment
history have a greater chance to be required by lenders to collateralised their loans. This is
consistent with predictions of SBOR suggesting that collateralisation is required and demandside determined. Even so, the SBOR paradigm cannot be fully supported by the results because
we also find supply-side effects. For example, borrowers in more profitable industry and more
experienced entrepreneurs have a higher likelihood of collateralising their loans. This reflects the
20
supply-side effects where, for instance, experienced entrepreneur are inclined to use collateral to
trade-off their interest payments on loans. Therefore, SBOR paradigm cannot be fully supported.
Table 4: around here please.
Following SBPI prediction, we regress the likelihood of collateralisation on loan characteristics
and private information, i.e. instrumented D&B score. We also disentangle borrower’s risk from
loan size effects by using different measures and interaction terms and the results are reported in
Table 5. Our interpretation is based on Model 1 as other models are rejected either by the
statistical insignificance of the model (Model 3) or by the insignificance of the exogeneity test
(Models 2 and 4). The results support the predictions of SBPI and suggest that where
endogenously determined interest rate is high, a borrower is more likely to pledge collateral in
order to trade-off the future interest payment on loans. Again, loan size has a positive and
significant impact on the likelihood of collateralisation. Most importantly, we find that the risk
level of a borrower, measured by instrumented D&B score, has a significantly negative impact on
the likelihood, implying that riskier borrowers, i.e. those having higher D&B scores, are less
likely to collateralise their loans. In other words, good (less risky) borrowers may self-select to
pledge collateral in order to trade-off interest payments. Hence, the empirical results reported
here are inconsistent with the empirical findings on small businesses (Berger and Udell, 1990)
and listed companies (Booth and Booth, 2006; Chen et al. 1998) where collateral is pledged by
risky borrowers who are charged higher interest rates. In contrast, our results suggest the supplyside, i.e. borrowers, play a determinant role in collateralisation and good borrowers use collateral
21
to trade-off interest payments on loans. Even so, we cannot conclude collateral is entirely
supply-side determined according to SBPI because we have not included the demand-side factors
in the same model.
Table 5: around here please.
The results of the test of SBPI suggest that private information does play an important role in
the determination of collateralisation. Whilst, according to our SBSS model, both private
information and observable signals ‡‡‡ would influence the contract terms of loans, from supplyside and demand-side, together. Thus, in the empirical test of SBSS, we include both
determinants in the regressions and the results are reported in Table 6.
Table 6: around here please.
Basically, Model 1 sheds more light on the determination of collateralisation because the
coefficients of the other measures of loan size by bands and the interaction terms between loan
size and borrower’s quality are not statistically significant. As a result, we base our following
interpretation on the results of Model 1. There are four key implications derived from the results.
Firstly, again, the endogenously determined interest rates charged on loans have a positive
‡‡‡
One may argue that the signal variables, i.e. characteristics of business and entrepreneur, are not observable
because the samples used in the regressions are those who borrowed before the end of financial year. In practice,
the signal variables we use here are essentially consistent over time. That is such variables do not change over time
or can be estimated easily by taking account of the time factor, such as gender, firm delinquent history and years of
experience. This weakness comes from the cross-sectional nature of the data.
22
impact on the likelihood of collateralisation, suggesting that borrowers may use collateral as a
means to trade-off interest payments on loans. This result supports H2 §§§ . Secondly, the
likelihood of collateralisation also depends upon the characteristics of the loans. For example,
larger loans, loans with longer maturity and vehicle/equipment loans are more likely to be
collateralised, implying a transaction motivated collateralisation either because such loans are
riskier or because the collateral is easily to evaluate. This result partially supports H3 which
indicates that there is a positive relationship between the amount of collateral and loan size.
Thirdly, inconsistent with the predictions of SBPI which focuses solely on the supply-side of
collateral, our results suggest that observable signals do have strong impacts on collateralisation
which can be understood from the demand-side. For example, borrowers, who had delinquent
history, i.e. bad signal, have a higher possibility of being required to pledge collateral on loans.
These results partially support H4. We also find that more experienced entrepreneurs have a
higher likelihood of collateralisation; while, male entrepreneurs have a lower likelihood, than
their counterparts. This possibly can be explained from the supply-side where experienced
entrepreneurs are supposed to be less risky and more likely to self-select a contract with collateral,
indirectly supporting H1. Fourthly, the negative sign of instrumented D&B score suggests that
the riskier the borrower (with higher D&B score), the less likely she collateralises her loan. This
result implies a self-selection mechanism by which borrowers make the collateralisation decision
according to their private information on their quality or risk levels. Thus, H1 is strongly
supported.
§§§
This is under the condition that a binary collateral variable is a good proxy for the true value of collateral, which
is an assumption adopted in most of empirical works; but this is doubted by recent studies, Hanley (2002) for
instance.
23
In summary, the results of the empirical tests of the three paradigms of collateralisation indicate
that SBOR and SBPI are not complete in interpreting loan collateralisation behaviour of small
business borrowers. The former focuses on the demand side factors and the latter focuses on the
supply side factors only. Indeed, SBSS sheds more light on collateralisation of small business
borrowing, which considers both demand side, i.e. ‘observable signals’, and supply side factors,
i.e. ‘private information’, simultaneously.
4.3 The Determination of Interest Rates
So far, we have examined the determinant effects of ‘observable signals’ and ‘private
information’ on the likelihood of collateralisation. In this sub-section, we examine the effects of
these two determinants on the interest rates charged on loans and the results are reported in
Table 7.
Table 7: around here please.
As shown, capital market variables have strong impacts on the interest rates charged. Prime rate
has insignificant impacts on interest rate; while similar to Petersen and Rajan (1994), we find
interest rate charged on small business loans would be high when the default spread **** is high.
****
The Prime Rate is obtained from the Federal Reserve and it reflects the basic risk-free rate of interest in the
financial market at the date on which the sample firms borrowed. The Default Spread is the difference between the
BAA corporate rate and the long-term government bond rate. This is the default premium for the bank’s best
customers, and these data are obtained from the database service of DataStream.
24
We also included market concentration †††† variables in the regression, but none is statistically
significant. This is possibly because existing literature has identified that market concentration
plays an important role in determining the availability of small business finance in the U.S. (e.g.
Petersen and Rajan, 1995), but probably a less important role in determining the cost of small
business finance. In contrast, Hanley et al (2006) reported that, in the U.K, market share creates
rents for banks and the lenders with the largest market share in SME finance charged
significantly higher interest premia.
The results reported in Table 7 also indicate that collateralised loans were charged lower rate,
supporting H2. This differs from Berger and Udell (1990) and Booth and Booth (2006) who
analysed aggregated data from banks and found that higher proportion of secured loans in
banks’ portfolios were positively related to risk premia on individual secured loans and chargeoff rates for banks. H3 is also supported where loan size is negatively related to interest rates.
This may reflect that it is more cost efficient for banks to manage a large loan than to manage a
large number of small loans. In terms of relationship effect, our result is consistent with that of
Berger and Udell (1990) but inconsistent with that of Petersen and Rajan (1994). Indeed, costs of
borrowing for small business borrowers can be significantly reduced by developing a longer
relationship with lenders and such relationship would alleviate the severity of asymmetric
††††
The competition within the local financial market is measured by a Herfindahl index, which is a categorical
variable. It is equal to one when the index locates between 0 and 1000, meaning the financial market is less
concentrated. It equals two when the index is between 1000 and 1800, suggesting a moderate concentrated financial
market and it equals three when the index is larger than 1800, meaning that the financial market is highly
concentrated.
25
information problem, partially supporting H5 ‡‡‡‡ . Finally, we find that borrowers, who
transferred good signals, such as larger employment size, greater personal wealth and more
experience, enjoy lower interest rates. In contrast, those who transferred bad signals, such as
owner’s delinquent history and higher D&B scores, were penalised by higher rates.
5. SUMMARY AND CONCLUSIONS
The 1990 paper by Berger and Udell made an important distinction between sorting-byobserved-risk (SBOR) and sorting-by-private-information (SBPI) as responses to asymmetric
information. The current paper seeks not to distinguish, but to integrate, these responses in what
we called Signalling and Self-Selection (SASS). The SASS model is one in which the type (high or
low) of the entrepreneur is private information known only to the entrepreneur and the bank
offers a menu of contracts as a self-selection mechanism. The SASS model proposes that hightype entrepreneurs, who have a high probability of success and high project returns, are more
likely to choose a contract with high collateral but low interest rate. Low-type entrepreneurs, on
the contrary, who have a low probability of success and low project returns, are more likely to
choose a contract with low collateral but high interest rate. The SASS model predicts that the
arrangement and choice of debt contracts is influenced by loan characteristics, signals transferred
by entrepreneurs, borrower’s quality and the relationship between the entrepreneur and the bank.
‡‡‡‡
Due to the limitations of the dataset, such as sample size and information available, we estimate the effect of
relationship lending without making a distinction between the case where bank observes good signals and the case
where bank observes bad signals.
26
In other words, both demand-side and supply-side factors would strongly affect the outcomes of
loan contact terms.
Using the 1998 Survey of Small Business Finances, we find that by including a proxy of ex post
risk measurement in the regression we can examine how private information influences the
offering of collateral from more informed entrepreneurs. The probit estimates suggest that such
private information strongly influences the collateralisation decision, with less risky
entrepreneurs being more likely to pledge collateral. This supports the prediction of Bester (1985)
and our SBSS model. This paper includes, for the first time, many personal characteristics of the
entrepreneur in regressions seeking to explain collateralisation and interest rates. It finds gender,
years of experience, personal wealth and credit history to be significant in at least one equation.
Unlike Petersen and Rajan (1994), we find that relationship lending significantly reduces the
interest rates charged on loans.
Our results imply that both the signalling process and the self-selection mechanism influence the
outcome of entrepreneurial debt finance, which in turn depends upon the scale of asymmetric
information. High type entrepreneurs are more likely to pledge collateral, supporting our theory
that the choice of contracts is determined by private information. It also seems that the signals of
the entrepreneur are as important as the signals of the business, since entrepreneurs with ‘good’
signals enjoy more favourable contracts than those with ‘bad’ signals. The evidence from this
paper emphasises that there are considerable returns to the ‘good’ entrepreneur, in conditions of
asymmetric information, in signalling her ability to the lender.
27
Appendix A: Proof of Proposition
Manipulating Equ. (8) by assuming a fully competitive capital market, we have
K θ − K + α Y H + (1 − α )Y L = 0 ……….(A.1);
where
θ = αθ H + (1 − α )θ L ………….(A.2),
Y H = rH θ H K + (1 − θ H )C H …………..(A.3),
Y L = rLθ L K + (1 − θ L )C L ……………..(A.4).
θ can be understood as the estimated entrepreneurial talent of the borrower and the expected
probability of success of the project undertaken by such an entrepreneur when a good signal is
observed. Y H and Y L can be interpreted as the expected (net) conditional transfer to the bank
from a high-type and a low-type entrepreneur, respectively. The expected net transfer, in the
event of success, is the interest payment multiplied by the likelihood of success, i.e., rθK; while
the net transfer, in the event of failure, is the value of collateral multiplied by the likelihood of
failure, i.e., (1-θ)C.
Rearranging the IR condition for high-type entrepreneur in Equ. (9), we have
EU H (ΓH ) = θ H K + W − Y H ≥ W ……..(A.5);
2
28
so
Y H ≤ θ H K ………………(A.6).
2
By the same logic, for a low-type entrepreneur, we have
Y L ≤ θ L K …………………(A.7).
2
(A.6) and (A.7) can be easily understood as that the expected net conditional transfer to the bank
must be no more than the expected net payoff of the entrepreneur by undertaking the project;
otherwise the entrepreneur would have a negative net payoff. The IR condition always binds in
the model and stipulates the upper bound of the expected net transfer from the entrepreneur to
the bank in terms of financing contract (r, C). Manipulating the participation condition of both
bank and entrepreneur under the conditions of competitive capital market and individual
rationality, then the expected net transfer of the entrepreneur should lie in the following intervals
[1 − θ − (1 − α )θ L ]K
2
α
≤ Y H ≤ θ H K ………..(A.8).
2
and
[1 − θ − αθ H ]K
2
≤ Y L ≤ θ L K ……………(A.9).
1−α
2
The entrepreneur would maximise her utility by paying back to the bank as little as possible if the
negotiation power lies with the entrepreneur in a competitive capital market. Combining the
29
bank’s participation condition, IR condition and the entrepreneur’s utility function, we have the
maximum amount of expected utility of the entrepreneur ( i = {L, H } ) is
max EU i (Γi ) = θ i K + W − min(Y i ) ……..(A.10)
2
[1 − θ − (1 − α )θ L ]K
2
where min(Y i ) =
α
.
Lemma 1 When the bank observes a good signal s , the high-type entrepreneur has a maximum
expected utility of
max EU H ( ΓH ) = θ H K + W −
2
[1 − θ − (1 − α )θ L ]K
2
α
………….(A.11);
whilst, the low-type entrepreneur has a maximum expected utility of
(1 − θ − αθ H ) K
……………(A.12),
max EU L ( ΓL ) = θ L K + W −
1−α
2
2
where θ = αθ H + (1 − α )θ L .
30
When a bad signal is observed, the bank’s expected profit function is similar to that when a good
signal is observed, EXCEPT the posterior probability distribution of the entrepreneur. Then the
bank’s participation condition is
Eπ = (1 − α )[θ H (1 + rH ) K + (1 − θ H )C H − K ] + α [θ L (1 + rL ) K + (1 − θ L )C L − K ] = 0 ..(A.13)
which is equivalent to
K θ − K + (1 − α )Y H + α Y L = 0 ………(A.14)
where
θ = (1 − α )θ H + αθ L …………(A.15),
Y H = rH θ H K + (1 − θ H )C H ……….(A.16),
Y L = rLθ L K + (1 − θ L )C L …………...(A.17).
Then, we have
[1 − θ − αθ L ]K
2
≤ Y H ≤ θ H K ……….(A.18)
1−α
2
and
[1 − θ − (1 − α )θ H ]K
2
α
≤ Y L ≤ θ L K ………….(A.19),
2
31
meaning that when s = s , the expected net conditional transfer to the bank by the high-type
[1 − θ − αθ L ]K
2
, θ H K ] , and that by the low-type entrepreneur is
1−α
2
entrepreneur is between [
[1 − θ − (1 − α )θ H ]K
2
between [
α
,θ L K ] .
2
Lemma 2 When the bank observes a bad signal s , the high-type entrepreneur has a maximum
amount of expected utility of
max EU H ( ΓH ) = θ H K + W −
2
(1 − θ − αθ L ) K
………….(A.20);
1−α
2
while the low-type entrepreneur has a maximum amount of expected utility of
max EU L ( ΓL ) = θ L K + W −
2
[1 − θ − (1 − α )θ H ]K
2
α
………..(A.21),
where θ = (1 − α )θ H + αθ L .
Manipulating this IC condition and the expected utility function of the entrepreneur in Equation
(4) we have
YH < rLθ H K + (1 − θ H )C L ………..(A.22)
which is equivalent to
32
θ H K (rL − rH ) > (1 − θ H )(C H − C L ) ………….(A.23),
where YH = {Y H , Y H } . By the same logic, for low-type entrepreneur, the IC condition is
YL < rH θ L K + (1 − θ L )C H ……………(A.24)
which is equivalent to
θ L K (rH − rL ) > (1 − θ L )(C L − C H ) …………….(A.25),
where YL = {Y L , Y L } . The intuition of the IC condition is direct, suggesting that high-type
entrepreneurs prefer ΓH than ΓL and low-type entrepreneurs are better off by choosing ΓL than
by choosing ΓH .
Combining the two IC conditions of (A.23) and (A.25), we have
1−θH
1−θL
(C H − C L ) < rL − rH <
(C H − C L ) ………..(A.26),
θH K
θLK
which can be rearranged as
⎧if
⎨
⎩if
rL > rH
rL < rH
then C H > C L
…………….(A.27).
then C H < C L
33
Lemma 3 When the type of entrepreneur is private information, unknown to the bank, the
menu of contracts offered by the bank for two types of entrepreneurs should include one
contract with a higher interest rate and lower collateral and the other with lower interest rate and
higher collateral.
As defined, the expected utility of the entrepreneur is
EU i (Γi ) = θ i K + W − riθ i K − (1 − θ i )C i …………(A.28)
2
where i = {L.H } . Then the marginal utility of the interest rate and the collateral requirement is
∂EU
= −θK < 0 ……………(A.29)
∂r
and
∂EU
= −(1 − θ ) < 0 ………….(A.30).
∂C
Equation (A.29) and (A.30) imply that the marginal disutility of the interest rate increases with
entrepreneurial talent θ, but the marginal disutility of collateral decreases with θ. Therefore, hightype entrepreneurs would pledge more collateral to take advantage of a lower interest rate.
Meanwhile, low-type entrepreneurs prefer lower collateral by paying a higher interest rate. This
conclusion is consistent with the finding of Bester (1985), in which project return is given by a
34
random variable rather than a function of entrepreneurial ability and investments as defined in
the current model.
Lemma 4 High-type entrepreneurs choose a contract ΓH with a lower interest rate and higher
collateral; while, low-type entrepreneurs choose a contract ΓL with a higher interest rate and
lower collateral.
Further from Lemma 4, we have
dr
1−θ
……………..(A.31),
| EU = −
dC
θK
which suggests that the high-type entrepreneur has a flatter utility function than that of the lowtype entrepreneur. In other words, the marginal rate of substitution (MRSr,C) between the interest
rate and the collateral is smaller for high-type entrepreneurs than for low-type entrepreneurs.
Thus, we summarize these findings so far by Proposition indicated in Section 1.
Q.E.D
35
Appendix B: Proof of Corollary 3
In the model α is a measure of information asymmetry between lender and borrower. This
problem can be alleviated by developing a stronger or longer relationship between the
entrepreneur and the bank (Berger and Udell, 1995). As defined in the model, α increases as the
problem is attenuated. Thus, by using Envelop Theorem on Equation (8), we have that when the
bank breaks even and s = s
drH
dα
Eπ
=−
∂Eπ / ∂α
π ( H ) − π ( L)
=−
………..(A.32)
αθ H K
∂Eπ / ∂rH
where π ( H ) = θ H (1 + rH ) K + (1 − θ H )C H − K , which is the bank’s expected profit by lending
to a high-type entrepreneur and π ( L) = θ L (1 + rL ) K + (1 − θ L )C L − K , which is the expected
profit of the bank by lending to a low-type entrepreneur. Because the bank would make more
profit by lending high-type entrepreneur than lending low-type entrepreneur, π (H ) is always
larger than π (L) . Thus, we have
drH
dα
Eπ
< 0 …………(A.33),
suggesting that when a good signal is observed and the information problem is alleviated, hightype entrepreneur enjoys a lower interest rate. By the same logic, we have
36
drL
dα
Eπ
=−
π ( H ) − π ( L)
∂Eπ / ∂α
=−
< 0 ………….(A.34),
(1 − α )θ L K
∂Eπ / ∂rL
which suggests that the low-type entrepreneur also enjoys a lower interest rate when the value of
α increases and s = s . When the bank observes a bad signal, by using the same methods we have
drH
dα
Eπ
=−
− π ( H ) + π ( L)
∂Eπ / ∂α
=−
> 0 …………(A.35),
∂Eπ / ∂rH
(1 − α )θ H K
meaning that high-type entrepreneur would pay a higher interest rate. While, for low-type
entrepreneur we have
drL
dα
Eπ
=−
− π ( H ) + π ( L)
∂Eπ / ∂α
=−
> 0 ……………..(A.36)
αθ L K
∂Eπ / ∂rL
suggesting that the low-type entrepreneur also suffers a higher interest rate when the value of α
increases and s = s . Accordingly, we have Corollary 3.
Q.E.D
37
Reference:
Berger, A.N. and Udell, G.F. (1990) Collateral, Loan Quality, and Bank Risk. Journal of Monetary
Economics 25, 21-42.
Berger, A.N. and Udell, G.F. (1995) Relationship Lending and Lines of Credit in Small Firm
Finance. Journal of Business 68, 351-381.
Bester, H. (1985) Screening vs Rationing in Credit Markets with Imperfect Information .
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Bester, H. (1987)
The Role of Collateral in Credit Markets with Imperfect Information.
European Economic Review 31, 887-899.
Booth, J.R. and Booth, L.C. (2006) Loan Collateral Decisions and Corporate Borrowing Costs.
Journal of Money, Credit and Banking 38, 67-90.
Cavalluzzo, K.S., Cavalluzzo, L.C. and Wolken, J.D. (2002)
Competition, Small Business
Finance, and Discrimination: Evidence from a New Survey. Journal of Business 75, 641679.
Chen, S.S., Yeo, G.H.H. and Ho, K.W. (1998) Further Evidence on the Determinants of
Secured versus Unsecured Loans. Journal of Business Finance and Accounting 25, 371-385.
de Meza, D. and Webb, D.C. (1987)
Too Much Investment: A Problem of Asymmetric
Information. Quarterly Journal of Economics 102, 281-292.
38
Evans, D.S. and Jovanovic, B. (1989) An Estimated Model of Entrepreneurial Choice under
Liquidity Constraints. Journal of Political Economy 97, 809-827.
Hanley, A. (2002) Do Binary Collateral Outcome Variables Proxy Collateral Levels? The Case of
Collateral form Start-ips and Existing SMEs. Small Business Economics 18, 315-329.
Hanley, A., Ennew, C. and Binks, M. (2006) The Price of UK Commercial Credit Lines: A
Research Note. Journal of Business Finance and Accounting 33, 932-938.
Holland, J. (1994) Bank Lending Relationships and the Complex Nature of Bank-Corporate
Relations. Journal of Business Finance and Accounting 21, 367-393.
Jaffee, D. and Russell, T. (1976) Imperfect Information, Uncertainty, and Credit Rationing.
Quarterly Journal of Economics 90 , 651-666.
Jaffee, D.M. and Russell, T. (1984) Imperfect Information, Uncertainty, and Credit Rationing: A
Reply. Quarterly Journal of Economics 99, 869-872.
Laitinen, E.K. and Laitinen, T. (1998) Cash Management Behavior and Failure Prediction.
Journal of Business Finance and Accounting 25, 893-919.
Petersen, M.A. and Rajan, R.G. (1994) The Benefits of Lending Relationships: Evidence from
Small Business Data. Journal of Finance 49, 3-37.
Petersen M.A. and Rajan, R.G. (1995) The Effect of Credit Market Competition on Lending
Relationships. Quarterly Journal of Economics 110, 407-773.
39
Stiglitz, J. and Weiss, A. (1981) Credit Rationing in Markets with Imperfect Information.
American Economic Review 71, 393-410.
Webb, D.C. (1991) Long-Term Financial Contracts can Mitigate the Adverse Selection Problem
in Project Financing. International Economic Review 32, 305-320.
40
Figure 1: Choice of Contracts
Interest rate
Bank’s indifference
curve in r and C
rL
Low-type
rH
High-type
Collateral
CL
CH
Figure 2: Contracts with different size of borrowing
Interest rate
Bank’s indifference
curve in r and C.
Small borrower
rSmall
Large borrower
rL arg e
Collateral
C Small
C L arg e
41
Table 1: Descriptive Statistics
Panel A: Characteristics of Business and Entrepreneur (N=3561)
Variable
Definition
BUSINESS CHARACTERISTICS
SIC_PROFIT
Industry profitability1
SIC_RISK
Industry risk1
HHI3_B1
Headquartered in a competitive banking market (0,1)2
HHI3_B2
Headquartered in a moderately concentrated banking market (0,1) 2
HHI3_B3
Headquartered in a highly concentrated banking market (0,1)2
C_FAGE
Firm age (years)
LOGFAGE
Natural log value of one plus C_FAGE
TOTEMP
Total employment number
LOGTOTEMP
Natural log value of one plus TOTEMP
TLBTA
Capital structure: total liability/ total business assets
LOGTLBTA
Natural log value of one plus TLBTA
C_ORPORATION
Business is incorporated (0,1)
FAMILY_OWNED
Family owned (0,1)
OWNER_MANAGED
Owner managed (0,1)
FIRM_DELINQUENT
Firm delinquent before (0,1)
DB_SCORE
Dun and Bradstreet score: categorical3
INST_DB2
Instrumented D&B score: weighted average4
ENTREPRENEUR CHARACTERISTICS
C_OAGE
Owner’s age (years)
LOGOAGE
Natural log value of one plus C_OAGE
C_EXP
Experience of owner in business (years)
LOGEXP
Natural log value of one plus C_EXP
DEGREE
Owner has a college degree or above (0,1)
MALE
Male owner (0,1)
MINOR
Minority owner (0,1)
Owner delinquent before (0,1)
OWNER_DELINQUENT
OWNER_JUDGE
Owner judged before (0,1)
PERWEAL2
Personal assets of owner (million $)5
LNPW2
Nature log value of one PERWEAL2
Min
Max
Mean
Median
Std. Dev.
-1.0400
0.1100
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.4538
0.7200
0.7600
1.000
1.0000
1.0000
104.0000
4.6540
482.0000
6.1779
13000000
16.3805
1.0000
1.0000
1.0000
1.0000
5.0000
4.1491
-0.4265
0.3218
0.0514
0.4249
0.5234
14.4412
2.4494
25.5268
1.8999
4520.26
0.5278
0.2491
0.8531
0.8964
0.1443
2.9700
2.6984
-0.4300
0.2800
0.000
0.0000
1.0000
11.0000
2.4849
5.0000
1.6094
0.4190
0.3499
0.0000
1.0000
1.0000
0.0000
3.0000
2.6503
0.2522
0.1273
0.2208
0.4944
0.4995
12.1092
0.7858
54.6001
1.5544
220067.61
0.9288
0.4325
0.3540
0.3048
0.3515
1.0402
0.4814
19.0000
2.9957
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
95.0000
4.5643
72.0000
4.2905
1.0000
1.0000
1.0000
1.0000
1.0000
115.0000
4.7536
50.7152
3.9216
19.2129
2.8036
0.5218
0.7352
0.1435
0.1171
0.0393
0.9317
0.4296
50.0000
3.9318
18.0000
2.9444
1.0000
1.0000
0.0000
0.0000
0.0000
0.2750
0.2429
11.2680
0.2221
11.7909
0.6953
0.4996
0.4413
0.3506
0.3216
0.1944
3.6020
0.5130
Note:
1.
2.
3.
Industry profitability and risk is calculated based on industry information between 1994 and 1998 derived from COMPUSTAT, where profitability is measured by industry
averaged pre-tax income to total assets ratio and risk is measured by the standard deviation of profitability between 1994 and 1998.
Concentration of banking market is measured by the Herfindahl Index which is a categorical variable and measures the degree of competition within the local financial market.
It is equal to one when the index locates between 0 and 1000, meaning the financial market is less concentrated. It equals two when the index is between 1000 and 1800,
suggesting a moderate concentrated financial market. It equals three when the index is larger than 1800, meaning that the financial market is highly concentrated.
Dun and Bradstreet score on risk is categorical with a range from 1 to 5, where 1 is ‘low risk’, 2 is ‘moderate risk’, 3 is ‘average risk’, 4 is ‘high risk’ and 5 is ‘significant risk’.
42
4.
5.
We estimate the instrumented D&B scores by conducting ordered logistic models on the business and entrepreneur variables and their credit history. The instrumented D&B
score (INST_DB2) is continuous and a weighted average of the possible categories where the weight is the probability of a sample firm falling into a specific category estimated
from an ordered logistic model. Detailed instrumentation process is available from the authors on request.
Personal wealth is defined as the total value of the owner’s home equity and the net worth of other assets.
Panel B: Characteristics of Loan and Banking Relationship (N=796)
Variable
PRIME_RATE
DFT_SPD
COLLATERAL
LOAN_SIZE
LOGLOANSIZE
LOAN_SIZE1
LOAN_SIZE2
LOAN_SIZE3
LOAN_SIZE4
INT_RATE
LOGINTRATE
FIXED_RATE
MRL_BANK
MATURITY
LOGMATURITY
MRL6_2
RELATION
LOGRELATION_MRL
INTERACTION TERMS
INTER1
INTER2
INTER3
INTER4
LOGINTER
Note:
1.
2.
Definition
Prime rate1
Default spread2
Loan is collateralized (0,1)
Loan size in $
Natural log value of one plus LOAN_SIZE
Loan size is smaller than $20,000 (0,1)
Loan size is between $20,000 and $50,000 (0,1)
Loan size is between $50,000 and $150,000 (0,1)
Loan size is larger than $150,000 (0,1)
Interest rate charged on loan
Natural log value of one plus INT_RATE
Interest rate is fixed (0,1)
The lender is a bank (0,1)
Length of maturity of loan in month
Natural log value of one plus MATURITY
Type of loan is capital lease, vehicle/equipment loan
Length of relationship with lender in month
Natural log value of one plus MRLR8
Min
7.7500
1.0750
0.0000
100
4.6151
0.0000
0.0000
0.0000
0.0000
0.9000
0.6419
0.0000
0.0000
1.0000
0.6931
0.0000
0.0000
0.0000
Max
9.0000
1713.0000
1.0000
24000000
16.9936
1.0000
1.0000
1.0000
1.0000
25.0000
3.2581
1.0000
1.0000
432.0000
6.0707
1.0000
480.0000
6.1759
Mean
8.2195
79.1594
0.6307
473966.58
11.1012
0.2839
0.2425
0.1771
0.2965
9.0440
2.2779
0.6595
0.6997
55.0327
3.5857
0.5289
71.0490
3.0391
LOAN_SIZE1* INST_DB2
LOAN_SIZE2* INST_DB2
LOAN_SIZE3* INST_DB2
LOAN_SIZE4* INST_DB2
LOGLOANSIZE * INST_DB2
0.0000
0.0000
0.0000
0.0000
9.8729
4.1410
4.0562
3.9394
3.8305
56.9231
1.1984
0.5446
0.3971
0.6263
29.6213
Median
8.2500
1.8430
1.0000
50000
10.8198
0.0000
0.0000
0.0000
0.0000
9.0000
2.3026
1.0000
1.0000
36.0000
3.6109
1.0000
36.0000
3.6109
0.0000
0.0000
0.0000
0.0000
28.5419
Std. Dev.
0.3266
355.8175
0.4829
1602505.87
1.8856
0.4512
0.4288
0.3820
0.4570
2.3706
0.2523
0.4742
0.4587
66.5379
1.0863
0.4995
90.6931
1.9946
1.4807
1.1078
0.9791
1.1262
6.7555
The Prime Rate is obtained from the Federal Reserve and it reflects the basic risk-free rate of interest in the financial market at the date on which the sample firms borrowed.
The Default Spread is the difference between the BAA corporate rate and the long-term government bond rate. This is the default premium for the bank’s best customers, and
these data are obtained from the database service of DataStream.
43
Table 2: Correlation Matrix
Note: * denotes statistical significant at 5% or lower.
Panel A: characteristics of business and entrepreneur (N=3561)
1
2
3
4
5
6
7
8
9
SIC_PROFIT
SIC_RISK
C_FAGE
TOTEMP
TLBTA
INST_DB2
C_OAGE
C_EXP
PERWEAL2
1
1.0000
-0.2415*
0.0643*
0.0251
0.0157
-0.0870*
0.0543*
0.0661*
0.0479*
2
3
4
5
6
7
8
9
1.0000
0.0303
0.1137*
-0.0033
-0.1064*
0.0399*
0.0130
-0.0020
1.0000
0.2405*
-0.0152
-0.5253*
0.4978*
0.6331*
0.1251*
1.0000
0.0212
-0.2068*
0.1382*
0.2125*
0.1935*
1.0000
0.0061
0.0340*
0.0442*
0.0108
1.0000
-0.4560*
-0.4681*
-0.1135*
1.0000
0.6944*
0.1092*
1.0000
0.1383*
1.0000
Panel B: Characteristics of business and entrepreneur, loan and relationship (N=796)
1
1.0000
-0.2375*
0.0766*
-0.0199
-0.0020
-0.1157*
0.0639
0.0453
0.0371
2
3
4
5
6
7
8
1.0000
0.0575
0.1781*
0.0213
-0.1077*
0.0582
0.0716*
-0.0137
1.0000
0.2302*
0.0369
-0.4754*
0.5336*
0.6574*
0.0801*
1.0000
0.1090*
-0.1530*
0.2192*
0.2677*
0.1001*
1.0000
0.0696*
0.0637
0.0218
-0.0033
1.0000
-0.3948*
-0.3942*
-0.0217
1.0000
0.7107*
0.0730*
1.0000
0.0706*
1.0000
PRIME_RATE
0.0495
-0.0667
-0.0024
-0.0508
0.0357
0.0252
0.0544
0.0081
-0.0057
1.0000
DFT_SPD
-0.0038
0.0132
-0.0759
0.0622
-0.0035
-0.0572
0.1568*
-0.0127
-0.0181
0.0042
0.0060
0.0678
-0.1925*
0.0473
0.4048*
-0.0385
0.3916*
-0.2046*
0.0410
0.0954*
-0.0084
0.0442
0.0025
-0.0080
-0.0303
0.0484
-0.1384*
0.2343*
-0.0288
-0.2952*
-0.0106
0.0872*
-0.1933*
0.0315
0.2105*
-0.0462
0.1337*
-0.2245*
0.0429
0.2896*
-0.0164
0.0258
-0.0792*
-0.0123
0.0180
0.1866*
-0.0265
0.0344
0.0201
-0.0083
1
2
3
4
5
6
7
8
9
SIC_PROFIT
10
11
12
13
14
15
SIC_RISK
C_FAGE
TOTEMP
TLBTA
INST_DB2
C_OAGE
C_EXP
PERWEAL2
LOAN_SIZE
INT_RATE
MATURITY
RELATION
9
10
11
12
13
14
15
1.0000
-0.0439
0.1014*
0.0222
-0.0016
1.0000
-0.1122*
0.0592
0.0045
1.0000
-0.0678
-0.1548*
1.0000
-0.0337
1.0000
44
Panel C: Bivariate correlation (N=796)
1
2
3
4
5
6
1
C_COPORATION
1.0000
2
FAMILY_OWNED
-0.1647*
1.0000
3
OWNER_MANAGED
-0.0523
0.1205*
4
FIRM_DELINQUENT
0.0397
0.0150
-0.0085
1.0000
5
DEGREE
0.1116*
-0.1472*
-0.1232*
0.0060
1.0000
6
MALE
0.0519
-0.0413
-0.0056
-0.0185
0.0917*
1.0000
*
*
7
7
8
9
10
11
12
13
14
15
16
1.0000
MINOR
-0.0949
0.0666
0.0464
0.0274
0.0985
-0.0041
1.0000
8
OWNER_DELINQUENT
-0.0564
0.0775*
0.0524
0.3807*
-0.0428
0.0051
0.0569
1.0000
9
OWNER_JUDGE
0.0026
0.0191
0.0577
0.0502
0.0300
0.0183
0.0559
0.0327
1.0000
10
COLLATERAL
0.0426
-0.0080
-0.0937
0.0656
0.0595
0.0473
-0.0691
0.0423
-0.0062
1.0000
11
LOAN_SIZE1
-0.1816*
0.1375*
0.1042*
-0.0794*
-0.1497*
-0.0891*
0.0052
0.0737*
0.0354
-0.1531*
1.0000
12
LOAN_SIZE2
0.0200
0.0084
*
0.1083
0.0161
-0.0227
0.0264
0.0014
-0.0159
0.0323
-0.1197
-0.3562*
1.0000
13
LOAN_SIZE3
0.0570
0.0065
-0.0227
0.0300
0.0316
-0.0123
0.0081
*
0.0724
-0.0263
0.0278
-0.2921
*
-0.2625*
1.0000
14
LOAN_SIZE4
0.1128*
-0.1492*
-0.1855*
0.0382
0.1427*
0.0735*
-0.0133
-0.1184*
-0.0432
0.2403*
-0.4088*
-0.3673*
-0.3012*
1.0000
15
FIXED_RATE
0.0010
-0.0144
-0.0004
0.0296
-0.1273
-0.0551
-0.0659
0.0314
-0.0155
-0.028
0.2231
*
0.0848
-0.0208
-0.2824*
1.0000
16
MRL_BANK
0.0103
-0.0281
-0.0746*
-0.0134
0.0499
-0.0109
0.0161
-0.0424
0.0259
-0.0186
-0.1164*
-0.0323
0.1029*
0.0592
-0.193*
*
*
*
*
1.0000
45
Table 3: Univatiate Tests
t test is conducted for continuous variables on mean and z test for binary variables on median.
SIC_PROFIT
SIC_RISK
C_FAGE
TOTEMP
TLBTA
C_CORPORATION
FAMILY_OWNED
OWNER_MANAGED
FIRM_DELINQUENT
DB_SCORE
INST_DB2
C_OAGE
Collateral=0 (N=294)
Collateral=1 (N=502)
p value
-0.4449
-0.4302
0.4619
0.3108
0.3369
0.0141
12.5986
14.6932
0.0092
27.6054
48.8088
0.0001
6.5980
3333.8630
0.4066
0.2993
0.3406
0.2298
0.7857
0.7789
0.8220
0.9150
0.8506
0.0082
0.1667
0.2211
0.0643
3.0238
2.9880
0.6683
2.7290
2.6564
0.0432
47.8197
50.2351
0.0018
16.9286
20.4223
0.0001
DEGREE
0.5306
0.5916
0.0934
MALE
0.7585
0.7988
0.1824
C_EXP
MINOR
OWNER_DELINQUENT
OWNER_JUDGE
PERWEAL2
PRIME_RATE
DFT_SPD
LOAN_SIZE
LOAN_SIZE1
LOAN_SIZE2
LOAN_SIZE3
LOAN_SIZE4
INT_RATE
FIXED_RATE
MRL_BANK
MATURITY
MRL6_2
RELATION
0.1361
0.0916
0.0514
0.0850
0.1116
0.2323
0.0238
0.0219
0.8620
1.4571
1.3548
0.8349
8.2245
8.2166
0.7435
77.4230
80.1764
0.9162
172512.4000
650515.5000
0.0001
0.3741
0.2311
0.0001
0.3095
0.2032
0.0007
0.1633
0.1853
0.4328
0.1531
0.3805
0.0001
9.4755
8.7913
0.0001
0.6769
0.6494
0.4299
0.7109
0.6932
0.5999
36.5034
65.8845
0.0001
0.3299
0.6454
0.0001
69.4388
71.9920
0.7017
46
Table 4: Tests of Sorting-by-Observed-Risk (SBOR) Paradigm
The dependent variable is
COLLATERAL
(0,1) and the probability modelled by PROBIT is
COLLATERAL=1.
specifications and the results of full models are available from the authors upon request. Base groups are
Reported here are the estimation results of models with restricted
LOAN_SIZE1, INTER1
and other type of loan.
***, **,
and * denote
statistical significant level of 1%, 5% and 10% respectively.
LOGLOANSIZE
Model 1
Observed
Bootstrap Std.
Coefficient
Err.
***
0.0582
0.2578
Model 2
Observed
Bootstrap Std.
Coefficient
Err.
LOAN_SIZE2
-0.0038
0.2147
LOAN_SIZE3
0.3367
0.2143
LOAN_SIZE4
0.9301***
0.2078
Model 3
Observed
Bootstrap Std.
Coefficient
Err.
LOGMATURITY
Model 4
Observed
Bootstrap Std.
Coefficient
Err.
0.1352*
0.0709
MRL6_2
0.8656***
0.1597
0.8273***
0.1420
0.8128***
0.1737
0.6289***
0.1565
SIC_PROFIT
0.4890**
0.2436
0.5052**
0.2241
0.5502**
0.2320
0.5894**
0.2992
SIC_RISK
1.1924**
0.5819
1.1392*
0.6120
1.3813**
0.6390
1.1779*
0.6804
0.0778*
0.0481
0.1103***
0.0390
0.0756
0.0651
0.3092**
0.1526
0.4675
0.3968
1.2300***
0.2701
0.0336**
0.0133
INTER2
-0.0532
0.0539
INTER3
0.0788
0.0844
INTER4
0.2772***
0.0665
-0.8712**
0.3564
LOGTOTEMP
LOGEXP
OWNER_JUDGE
0.1065
0.1923*
0.5466
0.4442
0.2666
0.5841**
LOGINTER
CONSTANT
Number of Observations
Wald Chi2
Log Likelihood
Prob>Chi2
Psuedo R2
-3.6196***
413
49.35
-223.3371
0.0000
0.1747
0.6960
-0.7087**
413
131.37
-225.4602
0.0000
0.1669
0.2968
-2.4106***
413
47.75
-232.1782
0.0000
0.1420
0.6750
384
83.43
-207.7955
0.0000
0.1522
Table 5: Tests of Sorting-by-Private-Information (SBPI) Paradigm
The dependent variable is
COLLATERAL
(0,1) and the probability (COLLATERAL=1) is modelled by probit models with endogenous covariates in order that the trade-off
between collateral and interests can be examined coherently. LOGINTRATE is instrumented by characteristics of loans and capital market concentration which is measured
by a Herfindahl index. Reported here are the estimation results of models with restricted specifications and the results of full models are available from the authors upon
request. Base groups are LOAN_SIZE1, INTER1 and other type of loan.
***, **,
and * denote statistical significant level of 1%, 5% and 10% respectively.
Model 1
Model 2
Model 3
Observed
Coefficient
Bootstrap
Std. Err.
Observed
Coefficient
Bootstrap
Std. Err.
LOGINTRATE
3.3417***
1.2895
2.6280
3.1533
LOGLOANSIZE
0.1559***
0.0263
Observed
Coefficient
Model 4
Bootstrap
Std. Err.
Observed
Coefficient
Bootstrap
Std. Err.
3.3324
3.8672
2.5206
2.7200
0.2397
0.3809
LOAN_SIZE2
0.1781
0.1997
1.1591
1.7152
LOAN_SIZE3
0.3336*
0.1983
0.5793
1.4924
LOAN_SIZE4
0.6568**
0.3261
1.8221
1.4227
MRL_BANK
-0.0321
0.2129
0.0657
0.2331
-0.0308
0.3762
0.0665
0.2701
LOGMATURITY
0.1167
0.0854
0.1790**
0.0868
0.1165***
0.0388
0.1852*
0.1148
MRL6_2
0.5631***
0.2048
0.6506*
0.2713
0.5655***
0.0475
0.6413**
0.2628
INST_DB2
-0.3759*
0.2085
-0.3141
0.3895
-0.0194
2.3269
-0.0690
0.6374
-0.0320
0.1518
-0.3587
-0.0839
-0.4394
-6.6258
0.6239
0.5056
0.4658
4.8260
LOGINTER
INTER2
INTER3
INTER4
CONSTANT
Number of observations
Wald Chi2
Log likelihood
Prob>Chi2
Wald test of exogeneity:
Chi2(1)
Prob > chi2
-8.7809***
2.4031
-6.1768
6.2890
-9.7014***
2.4779
360
110.38
-191.9772
0.0000
360
9.25
-195.3085
0.3213
360
10.36
-191.646
0.3782
360
11.19
-192.2038
0.4272
7.61
0.0058
1.96
0.1618
7.51
0.0061
1.94
0.1641
48
Table 6: Tests of Sorting-By-Signalling-and-Self-Selection (SBSS) Paradigm
The dependent variable is
COLLATERAL
(0,1) and the probability (COLLATERAL=1) is modelled by probit models with endogenous covariates in order that the trade-off
between collateral and interests can be examined coherently. LOGINTRATE is instrumented by characteristics of business, entrepreneur, loans and capital market concentration
which is measured by a Herfindahl index. Reported here are the estimation results of models with restricted specifications and the results of full models are available from the
authors upon request. Base groups are LOAN_SIZE1, INTER1 and other type of loan. ***, **, and * denote statistical significant level of 1%, 5% and 10% respectively.
Model 1
LOGINTRATE
LOGLOANSIZE
Model 2
Bootstrap Std.
Err.
Observed
Coefficient
Bootstrap Std.
Err.
Observed
Coefficient
Bootstrap Std.
Err.
Observed
Coefficient
Bootstrap Std.
Err.
2.8369*
0.1510***
1.6664
0.0351
2.4733
2.1952
2.8136
0.2105*
1.7954
0.1247
2.3012
3.0083
0.0456
0.2307
0.3869
0.2249
0.6120***
0.0820
0.5708**
0.3014
-0.3336
-0.4998
0.2001
0.1866
0.2556
0.1577
0.1458
0.0662
0.2966
0.1417
0.2641
0.3870
1.3606
0.4087
1.2828
0.2354***
0.5984***
0.0780
0.5869
0.3060*
-0.3025
-0.2620
1.8917
1.8133
1.6807
0.0873
0.1628
0.0935
0.3678
0.1638
0.2852
0.7621
-0.4906
-0.0620
-0.3360
-6.4882
0.7294
0.6347
0.5703
5.3103
LOAN_SIZE3
LOAN_SIZE4
MRL6_2
0.1772**
0.6337***
0.0898
0.1838
0.5290*
0.3158**
-0.3465***
-0.5048*
0.3495
0.1421
0.1287
0.2821
LOGTOTEMP
FIRM_DELINQUENT
LOGEXP
MALE
INST_DB2
Model 4
Observed
Coefficient
LOAN_SIZE2
LOGMATURITY
Model 3
LOGINTER
0.1773***
0.6355***
0.0626
0.2263
0.5298*
0.3142*
-0.3408**
-0.2539
-0.0226
0.2996
0.1722
0.1612
0.6060
0.0491
INTER2
INTER3
INTER4
CONSTANT
Number of observations
Wald Chi2
Log likelihood
Prob>Chi2
Wald test of exogeneity:
Chi2(1)
Prob > chi2
-8.1706**
3.6489
-6.1752
4.1601
4.1060
-8.7818**
360
84.96
-172.3793
0.0000
360
37.80
-172.8302
0.0001
360
27.57
-172.2002
0.0011
360
193.94
-169.4575
0.0000
7.86
0.0050
4.49
0.0342
8.07
0.0045
3.78
0.0518
49
Table 7: The Determinants of Interest Rates Charged
The depended variable is INT_RATE, i.e. the interest rate charged on loan. The models conducted are OLS.
INTERCEPT
DFT_SPD
COLLATERAL*
LOGLOANSIZE
LOGRELATION_MRL
SIC_PROFIT
SIC_RISK
LOGTOTEMP
LNPW2
LOGEXP
MINOR
OWNER_DELINQUENT
INST_DB2
Coefficient
Std. Err.
t
Pr>t
11.0663
0.0005
-1.1734
-0.1249
-0.1115
-0.4328
0.6366
-0.1112
-0.2343
-0.2381
0.4973
0.9413
0.3222
0.9227
0.0002
0.5815
0.0534
0.0391
0.2899
0.5445
0.0612
0.1459
0.1436
0.2633
0.2917
0.1930
11.99
2.15
-2.02
-2.34
-2.85
-1.49
1.17
-1.82
-1.61
-1.66
1.89
3.23
1.67
0.0001
0.0318
0.0440
0.0196
0.0045
0.1359
0.2428
0.0697
0.1088
0.0978
0.0593
0.0013
0.0956
Number of observations
F test
Prob > F
R2
Adj-R2
Note:
*
To overcome the endogeneity problem,
743
12.20
0.0001
0.1668
0.1531
COLLATERAL
is instrumented by observable signals, loans characteristics and
borrower’s quality. The instrument model and results are available from the authors upon request.