Abstract
We analyze under what conditions competitive credit markets are efficient in providing loans to entrepreneurs who can start a new project after failure. An entrepreneur of uncertain talent chooses the riskiness of her project. If banks privately observe the entrepreneur’s risk choices, two equilibria coexist: (1) an inefficient equilibrium in which the entrepreneur realizes a low-risk project and has no access to finance after failure and (2) a more efficient equilibrium in which the entrepreneur first realizes high-risk projects and then, after continuous failures, a low-risk project. There is a non-monotonic relationship between bank information and potential credit market inefficiency. We discuss the implications for credit registers and entrepreneurial education.
1 Introduction
What determines the level of entrepreneurial activity in an economy? One key variable is the extent to which failed entrepreneurs are excluded from further entrepreneurial finance. European and Japanese financiers, for instance, are perceived to be more reluctant to finance a failed entrepreneur’s restart than their American counterparts. It therefore has become commonplace to praise the US’ lower “stigma of failure” as the source of its higher entrepreneurship rates[1] and consequently of its competitive edge in terms of the ability to innovate, commercialize and grow.[2]
In this paper, we present endogenous risk choice as an explanation for why economies with identical institutional, legal and cultural constraints can experience different levels of the “stigma of failure”. If the “stigma of failure” is high and banks provide credit only to those who have never failed, entrepreneurs will choose low-risk projects. In this economy, failure indicates low entrepreneurial talent. If the “stigma of failure” is low and banks provide credit to failed entrepreneurs, new entrepreneurs will be more inclined to experiment with novel (and more risky) business ideas. Failure at the beginning of an entrepreneurial career then indicates bad luck rather than low entrepreneurial talent.
To get an intuition for the model, imagine an entrepreneur who can undertake one of two projects, a low-risk project or a high-risk project. Both projects have no investment costs. The low-risk project yields a safe net present value (NPV) of
This logic is typical for optimal strategies in sequential search problems (Weitzman 1979). Projects where high payoffs occur with low probability may be investigated first, even though their expected value is smaller than that of projects with lower variance. As in the example above, the high-risk project should be undertaken first, because if it succeeds, the highest possible payoff is obtained; and if it fails, one can still realize the low-risk project. In contrast, if one starts with the low-risk project immediately, the low payoff occurs with certainty.
In our model, there are two barriers to optimal search. First, there are investment costs that cannot be financed by the entrepreneur herself. She has to apply for a loan on a competitive credit market. Second, her entrepreneurial talent, which is either high or low, influences her probability of success, but is unknown to her and to banks. Only the distribution of talent is common knowledge. The entrepreneur and banks learn about her talent from the outcome of the project. However, learning depends on the project’s risk: failure with a low-risk (high-risk) project implies a relatively low (high) probability of high talent. Given that the ex-ante probability of high talent is sufficiently large, the first-best outcome is as follows. The entrepreneur first undertakes high-risk projects. After continuous failures, she undertakes the low-risk project. Failure with the low-risk project discloses low talent; therefore, she stops undertaking projects at all.
Under what circumstances is the first-best an equilibrium outcome and what other equilibria exist? To answer this question, we consider three different informational settings: perfect information (PI), private information of banks (PIB) and imperfect information (IM). The equilibrium outcome is efficient when banks have perfect information about the riskiness of past and present projects. However, if banks only observe the risk of projects in their own loan portfolio (PIB), two equilibria may co-exist. First, an equilibrium in which the entrepreneur undertakes a low-risk project and, if it fails, does not get any more loans. Second, an equilibrium in which the entrepreneur first undertakes high-risk projects and then, after continuous failures, a low-risk project. The reason why the first assessment is an equilibrium is that only the lending bank observes the entrepreneur’s risk choice. Even if she undertakes a high-risk project, this bank becomes a monopolistic supplier of finance in case of failure and then can extract all future rents from her. This equilibrium is inefficient since the entrepreneur undertakes the low-risk project too early. Thus, countries with the same average entrepreneurial talent and institutional environment can experience different levels of the “stigma of failure”.
Under IM, banks never observe the risk of projects. This causes a moral hazard problem. The entrepreneur undertakes a low-risk project only if the expected payoff of the high-risk project is sufficiently small relative to that of the low-risk project. As under PIB, multiple equilibria may exist. However, in contrast to PIB, if the expected payoff of the high-risk project is close to that of the low-risk project, the entrepreneur will only undertake high-risk projects in equilibrium. If the ex-ante probability of high talent is sufficiently large, multiple rounds of project financing must occur in equilibrium. Consequently, the relationship between bank information and potential credit market inefficiency can be non-monotonic. Under PI, the outcome is always efficient. Under PIB, there is always an inefficient equilibrium with only one period of project financing. This equilibrium may be strictly dominated by any equilibrium under IM since in these equilibria the entrepreneur realizes several high-risk projects. In other words, the opportunity to shift risks constrains the maximal credit market inefficiency.
Our model yields a number of implications. It shows that the credit market outcome may be inefficient even if there is no asymmetric information between the entrepreneur and the bank that finances her project. The inefficiency is caused by the fact that outside banks cannot observe the entrepreneur’s risk choice. The model therefore highlights the role of information sharing. If banks are required to share their evaluation of E’s project risk with the market, banks would again have perfect information and the equilibrium outcome would be efficient.
Even if banks only share information about the loan rates of previously chosen contracts through credit registers, this could have a positive effect. Such information transmits the entrepreneur’s risk choice to the extent that if the entrepreneur chose a contract with a very low loan rate, this may indicate that she undertook a low-risk project (otherwise, the bank that offered this contract would have made negative expected profits). In this case, banks stop offering loans. Hence, a credit register may ensure the existence of an equilibrium in which the entrepreneur undertakes projects as in the case of PI.
Finally, our results imply that the potential welfare gains from an increase in the population’s average entrepreneurial talent might not fully be realized. If banks do not adjust their financing policies, entrepreneurs may end up choosing inefficiently low-risk levels.
The paper that comes closest to ours is Landier (2006). In his model, banks cannot distinguish between entrepreneurs with low ability who start a new venture because the previous one failed and entrepreneurs with high ability who are not bankrupt, but would like to start a more promising project. This can generate equilibria in which few (many) high-ability entrepreneurs restart and loan rates are high (low). Our model differs significantly from Landier (2006). First, banks always can observe how many times the entrepreneur went bankrupt. This assumption seems appropriate since information about bankruptcy is shared among banks in most developed countries. Second, the multiplicity of equilibria is caused by the interaction of the entrepreneur’s risk choice with banks’ beliefs about her action (and not by asymmetric information about her talent). Consequently, our model generates a number of new results about the impact of institutions on credit market outcomes.
The remainder of the paper is organized as follows. Section 2 relates the paper to the literature. Section 3 introduces the model and characterizes the first-best outcome. Section 4 examines the equilibrium set under PI, Section 5 under PIB, and Section 6 under IM. Section 7 discusses the implications of the model. All proofs are in the Appendix.
2 Related Literature
A considerable empirical literature tries to explain cross-country differences in the “stigma of failure” by using persistent institutional, legal or cultural characteristics.[4] Evidence confirms that fresh starts are affected by bankruptcy laws (Armour and Cumming 2008). The debate persists over which and how cultural traits shape attitudes towards entrepreneurial failure (Licht and Siegel 2006; Hayton, George, and Zahra 2002; Giannetti and Simonov 2004; Singh, Corner, and Pavlovich 2015).[5] Our contribution is to present a model that endogenizes the “stigma of failure”.
Two other papers study models of entrepreneurial finance with asymmetric information and find multiple equilibria. Gromb and Scharfstein (2002) analyze an occupational choice model in which agents either become entrepreneurs or intrapreneurs. When there are few (many) entrepreneurs, the average quality of failed entrepreneurs is low (high). As a result, the external labor market (that offers jobs to failed entrepreneurs) is poor (good), so that few (many) agents start a venture on their own. Ghatak, Morelli, and Sjostrom (2007) consider a general equilibrium model in which wages for dependent labor are low (high) when there are many (few) untalented entrepreneurs, which implies that many (few) agents become entrepreneurs. In contrast to these papers, we endogenize the number of rounds banks are willing to finance an entrepreneur after failure. The driver of our results is the link between risk choice and bank lending. New entrepreneurs will choose risky (safe) projects provided that banks (do not) finance projects after failure. Consequently, the average talent of failed entrepreneurs is high (low), such that multiple rounds of project financing (do not) occur in equilibrium.[6]
We also contribute to the literature on entrepreneurial risk-taking. A common explanation why entrepreneurs often bear substantial undiversified risk despite the lack of a positive premium, is (over-)optimistic beliefs (see, e.g. Landier and Thesmar 2009). Vereshchagina and Hopenhayn (2009) interpret entrepreneurial risk-taking as a lottery over future wealth that is chosen by borrowing-constrained agents. Limited liability then makes poor and impatient agents (who have not yet saved much) take more risk. Campanale (2010) rationalizes entrepreneurial risk-taking on the grounds that entrepreneurs usually make small personal investments and gain large human capital from starting a business. In our model, risk-taking is determined by the willingness of banks to finance new projects after failure.
3 The Model
We consider an economy populated by an entrepreneur E and banks
3.1 The Entrepreneur
In period 0, nature decides on E’s entrepreneurial talent
3.2 Banks
Banks compete in a Bertrand manner by offering loan contracts. Their net refinancing costs are normalized to 0. Our solution concept is sequential equilibrium (SE). We therefore assume finite actions sets. Let the set of possible loan rates be given by
3.3 Strategies and Beliefs
Denote by
An SE (assessment), in which E undertakes and banks finance the high-risk project in the first
3.4 The First-Best Outcome
Assume for a moment that
Solving for
Now imagine that E has “deep pockets” and
for each
Since
There is a function
(i) only if she chooses
See Appendix. ■
We will refer to
4 Perfect Information (PI)
We first consider a setting with PI, in which banks can observe all of E’s risk choices. Note that if
If
5 Private Information of Banks (PIB)
5.1 Multiple Equilibria
We now relax the assumption that banks can perfectly observe the riskiness of all past projects. Instead, a bank can only observe the risk of projects in its own loan portfolio. The risk of projects in other banks’ portfolios remains unknown. Therefore, a lending bank acquires private information about E.
Consider an assessment in which E chooses
Moreover, an efficient SE with
There can also be equilibria with more than one period of project financing. Consider a
Let
See Appendix. ■
5.2 Credit Registers
We now assume the existence of a credit register that informs all banks about the loan rates of E’s previously chosen loan contracts. When E chooses contract
Consider a
Next, let there be a credit register. If E deviates and chooses a contract
Suppose that
See Appendix. ■
5.3 A Numerical Example
The following example illustrates these results (see the Appendix for details). Let
Total expected payoff of the
Let us consider the equilibrium set in this example. Under PI, the maximal expected payoff is realized: for small values of the high-risk project’s profit (
A credit register that informs banks about the loan rates of chosen contracts can make a difference in the example. The requirement
6 Imperfect Information (IM)
We now turn to the setting with IM, in which no bank can observe E’s risk choices. It is no longer possible for banks to restrict
Under IM, banks face a moral hazard problem. E may be inclined to shift risk and undertake the high-risk project when banks offer loan contracts that guarantee non-negative profits only if E chooses the low-risk project. We will see that this moral hazard problem sometimes eliminates those inefficient equilibria where E realizes the low-risk project too early.
Consider an assessment in which E chooses
Rearranging this inequality yields
Banks make non-negative profits only if
The interpretation of
6.1 Equilibria if ( A 3 )
We just derived that when
As E keeps failing with high-risk projects, banks’ assessment of her ability worsens. We define the maximum number of periods banks are willing to offer loan contracts to E (given that E always chooses the high-risk project) by
We now can state:
If
Clearly, an equilibrium in which E always realizes high-risk projects is not efficient. In the period before banks stop offering loans, E would prefer to undertake the low-risk project when the loan rate is adjusted accordingly. Unable to commit to choosing
However, total expected payoffs in the equilibrium under IM can be much larger than in the inefficient
Total expected payoff of the
Consider again the example from Section 5.3. Figure 2 displays the total expected payoff in the
6.2 Equilibria if ( A 3 )
When
Consider first a
Next, consider a
Again, an efficient equilibrium may not exist under IM. The reason is that the common belief about E’s talent in period
Let
See Appendix. ■
7 Discussion
We have analyzed a model of entrepreneurial finance and risk-taking where the extent to which failed entrepreneurs are excluded from further financing is determined endogenously. The driver of our results is the evolution of banks’ beliefs about an entrepreneur’s talent and the interplay between these beliefs and her risk choices. If banks can perfectly observe the entrepreneur’s actions, then the first-best outcome is realized in any equilibrium: she first undertakes a number of high-risk projects and then, after continuous failure, undertakes a low-risk project.
When banks acquire private information about E’s risk choices, the first-best outcome is not the unique equilibrium outcome. Instead, there also exists an inefficient equilibrium in which the entrepreneur undertakes a low-risk project and becomes excluded from finance after failure. This inefficiency is due to the fact that banks may expect the entrepreneur to undertake the low-risk project. Failure of low-risk projects indicates low talent. Therefore, outside banks may refuse to finance her after failure. The bank that financed the project then becomes a monopolistic supplier of finance to the entrepreneur. Hence, it is rational for the entrepreneur to undertake a low-risk project.
We also saw that the opportunity to shift risks (when banks cannot control the project risk) may increase welfare as compared to the case when only the financing bank controls the project risk. If banks do not observe the riskiness of projects (i.e. banks cannot acquire private information about
In the following, we discuss several implications of our model.
7.1 Asymmetric Information
The notion that asymmetric information can lead to an inefficient allocation of credit is well-established in economic theory. The financial contracting literature has focused on solutions of the moral hazard problem if banks cannot directly observe E’s risk choice (via monitoring, collateral or incentive contracts). We have shown that the credit market equilibrium can be inefficient even if there is no asymmetric information between E and the bank that finances her project. This inefficiency is caused by the feedback loop between risk-taking and outside banks’ beliefs. Policies that aim to change the nature of the equilibrium may not be effective, as both entrepreneurs’ actions and banks’ expectations would have to be changed simultaneously. Consider, for example, the approach of the European Commission (2000; 2007). It attempts to reduce the “stigma of failure” by advising entrepreneurs to choose higher risk levels. Entrepreneurs, however, will follow such advice only if financiers change their policy at the same time.
7.2 Sharing Information
Our model has novel implications for credit registers and their informational content. So far, the literature has shown that credit registers flagging failure increase credit market efficiency because they resolve the adverse selection problem (Pagano and Jappelli 1993; Padilla and Pagano 1997). We show that a credit register that merely reports bankruptcy history may not be enough to remove inefficient equilibrium outcomes. When banks acquire private information about E’s risk choices, an equilibrium arises where the bank that finances E’s project will hold up E after failure, which in turn leads to the (inefficient) realization of low-risk projects at an early stage of E’s career.
A possible way out of this trap is to promote information sharing among banks. If the incumbent bank truthfully shares its evaluation of E’s project with the market, we are again back in the setting with perfect information where in equilibrium E first experiments with risky business ideas before she realizes the low-risk project. Thus, information sharing can increase entrepreneurial activity. Note that information sharing would not impact on banks’ profits in our setting.
If the truthful communication of E’s previous risk choices is not feasible, the exchange of information about contract details through credit registers may also increase credit market efficiency. As we emphasized in Section 5, information about the loan rates of previous contracts can be crucial for ensuring the existence of more efficient credit market equilibria. This information enables banks to infer E’s previous risk choices from loan rates. An unpaid loan with a relatively low loan rate may indicate that the underlying project risk was low (otherwise, the bank would not have offered this loan to the entrepreneur). Failure then discloses low entrepreneurial talent, preventing banks from granting further loans to her. In contrast, an unpaid credit with a high loan rate may indicate that the underlying project’s risk was high, suggesting that its failure owes more to bad luck rather than low entrepreneurial talent. In this case, E probably deserves another chance. However, note that the loan rate alone does not reveal E’s actions. Banks might also infer from a high loan rate that E undertook the low-risk project and – by mistake – chose an inappropriate contract. Therefore, the multiplicity of equilibria persists as long as banks do not perfectly observe E’s risk choices.
7.3 Improving Entrepreneurial Talent
Our model suggests that the maximal number of times an entrepreneur can start anew after bankruptcy increases in entrepreneurs’ average talent (see Lemma 1). Hence, one measure to increase entrepreneurial activity is the promotion of education that leads to the formation of relevant skills. Entrepreneurial education plays a substantial role both in economic development (Bjorvatn and Tungodden 2010; Klinger and Schündeln 2011) and the EU’s policy to increase entrepreneurship after failure (European Commission 2007). In terms of our model, these policies would increase the probability of having high entrepreneurial talent
Appendix
A.1 A.1 Proof of Lemma 1
Take
and for
where
To prove the second claim, observe that
for all
A.2 A.2 Proof of Proposition 2
Let
and consider an assessment
In period 1, a bank
[15]A bank
A bank that financed the project in period 1 has a belief in period 2 that is derived from Bayes’ rule. As long as it is profitable, this bank offers contracts with loan rates equal to
E undertakes projects whenever possible.
which is implied by
In each period
[17]where
In period
Banks offer no contracts in any period
Whenever banks offer contracts as described above, E undertakes a high-risk project in all periods
For
Thus,
A.3 A.3 Proof of Proposition 3
The proof of existence of a
In period 1,
In each period
[20]where
In period
Banks offer no contracts in any period
Whenever banks offer contracts as described above, E undertakes a high-risk project in all periods
and in a period
Note that for
and
We can transform [23] into
and [24] into
Thus, it never pays off for E to choose a contract
Assumption
This inequality can be used to show that [27] follows from
A.4 A.4 Proof of Proposition 5
The proof is very similar to the proof of Proposition 2 and therefore omitted.
A.5 A.5 Details of the Numerical Example
PIB. We set
| t = 1 | 1.0929 | 1.6814 | 0.9000 |
| t = 2 | 1.2335 | 1.8977 | 0.7773 |
| t = 3 | 1.5654 | 2.4082 | 0.5751 |
| t = 4 | 2.2594 | 3.4760 | 0.3442 |
We can verify for each pair
In each period
[29]unless
In period
Banks offer no contracts in any period
Whenever banks offer contracts as described above, E undertakes a high-risk project in all periods
IM. In any equilibrium, E realizes the high-risk project (given that it gets financed) if the lowest possible equilibrium loan rate,
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Note
The views expressed herein are those of the authors and should not be attributed to the IMF, its Executive Board, or its management, or to the Federal Reserve Bank of Boston or Federal Reserve System. We thank Guido Friebel (the editor) and an anonymous referee for useful advice; Viral Acharya, Bruno Biais, Patrick Bolton, Douglas Gale, Hans Peter Grüner, Markus Kinateder, Holger Müller, Nicola Persico, Rafael Repullo, Sebastian Schäfer, Christian Schmieder, Ernst-Ludwig von Thadden as well as seminar participants at Pompeu Fabra, Goethe-University Frankfurt, Mannheim University and Federal Reserve Bank of Kansas City for valuable discussions and helpful comments. All remaining errors are our own.
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