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 Papers are produced in order to bring the results of research in progress to a wider audience and to facilitate discussion. They will normally be published in a revised form subsequently and the agreement of the authors should be obtained before referring to its contents in other published works. The Director of the CSME, Professor David Storey, is the Editor of the Series. Any enquiries concerning the research undertaken within the Centre should be addressed to: The Director CSME Warwick Business School University of Warwick Coventry CV4 7AL e-mail david.storey@wbs.ac.uk Tel. 024 76 522074 ISSN 0964-9328 – CSME WORKING PAPERS Details of papers in this series may be requested from: The Publications Secretary CSME Warwick Business School, University of Warwick, Coventry CV4 7AL e-mail sharon.west@wbs.ac.uk Tel. 024 76 523692 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. 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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.