1 Introduction

Banks often cannot observe ex ante failure probabilities of potential borrowers. To deal with this informational asymmetry, banks may offer incentive-compatible contracts with collateral to induce borrowers to disclose their private information. Based on this disclosure and therefore self-selection in one of the two groups: Low-risk borrower or high-risk borrower, banks decide to grant or deny credit, respectively. Typically, theoretical models show that private information is fully disclosed in equilibrium, since high-risk and low-risk borrowers self-select by choosing different contracts. Low-risk borrowers choose higher collateral at a lower interest rate, while high-risk borrowers select contracts without collateral at a higher rate. The key is that the cost of investing in collateral is lower for low-risk borrowers as they have a lower probability of failure (See Comeig et al. 2014 for an empirical test on this theory).

However, this self-selection is achieved when potential borrowers are identical in every respect other than failure probability (Bester 1985). Smart (2000) shows that the addition of the customer’s degree of risk aversion can change the nature of equilibrium, and different risk classes may be pooled at a single contract in equilibrium (See also Finkelstein and McGarry 2006 for empirical results). Specifically, risk averse low-risk borrowers may not be willing to accept higher collateral to self-select. The reason is that the collateral choice is also closely connected to the degree of risk aversion (See Cohen and Einav 2007; Barseghyan et al. 2011). The higher the risk aversion the lower the willingness to accept higher collateral to self-select. Low collateral exposes individuals to a lower risk by paying a higher contract price (interest rate).

Women are generally found to be more risk averse than men in financial decision-making. For example, women have been found to be more risk averse in financial decisions in downside risk environments (Comeig et al. 2015), with respect to the pension allocation decision (Bajtelsmit et al. 1999), to have less risky asset portfolios than men (Halko et al. 2012; Jianakoplos and Bernasek 1998), and to report lower willingness to accept financial risk (Barsky et al. 1997). Similarly, laboratory experimental tests also showed that women are more risk averse than men in financial decision-making (See Charness and Gneezy 2012, Croson and Gneezy 2009, and Eckel and Grossman 2008, for a review).

If this is the case, women might not accept higher collateral to self-select. Thus, women’s contract choices, even being rational decisions for low-risk borrowers, will wrongly classify women as high-risk borrowers, in those generally accepted models. Whether men and women systematically differ in their contract choices in the self-selection mechanism with collateral is an important economic question leading to potential women credit rejections and creating an institutional barrier to female entrepreneurship. Additionally, from the bank’s point of view, the women’s reluctance to accept high collateral generates an adverse selection problem. Particularly risk averse individuals (i.e., women wrongly classified here as high-risk borrowers) might also be the best borrowers for the bank.

In this paper, we conduct a laboratory experiment on financial decision-making in three different European countries, specifically designed to study systematic gender differences in credit self-selection.

Results show that incentive-compatible contracts with collateral fail to disclose women’s private information, while they disclose men’s private information. Thus, low-risk women consumers do not self-select as “theoretical” good borrowers. Beside this contribution, results show that gender differences arise when subjects face low failure probabilities (90% success probability), i.e., downside risk as defined by Comeig et al. (2015), a small probability of a relatively low payoff.

Just a few experimental papers have focused on this self-selection mechanism: (i) Capra et al. (2009) have studied the effects of moral hazard on choices on incentive-compatible credit contracts with collateral and (ii) Bediou et al. (2013) have analyzed framing effects in the same incentive-compatible contracts. This paper’s approach is different. None of the previous experiments have studied the effect of gender on credit contract choices.

The remainder of the paper is organized as follows. The next section, Sect. 2, presents the review of the literature and the hypotheses. Section 3 shows the experimental design. Section 4 presents the results from the experiment, and the final section, Sect. 5, summarizes the main conclusions and presents implications that affect both academics and practitioners.

2 Review of literature and hypotheses development

The theoretical model of Bester (1985) on credit screening and self-selection considers a credit market with risk neutral firms, which can either be low risk (high probability of repaying the loan) or high risk (low probability of repaying the loan). In this model, banks cannot ex ante screen borrowers by risk, due to the asymmetric information context (only borrowers know their risk level). However, banks can force the borrower's self-selection by offering them a pair of incentive-compatible contracts, (a) and (b):

  1. (a)

    Has low interest rate and high collateral.

  2. (b)

    Has high interest rate and low collateral.

Bester (1985) concludes that low-risk firms differentiate themselves from high-risk firms by accepting contract (a), with higher collateral. The reason is that collateral has a higher cost for those firms that may lose it, i.e., the high-risk firms.

As pointed out, this self-selection mechanism is achieved when borrowers are risk neutral. However, empirical and experimental studies have generally found that women are significantly more risk averse than men in financial decision-making; especially in downside risk decisions (Comeig et al. 2015), where there is a small probability of a relatively low payoff. Note that a low-risk borrower choosing loan contract (b), as defined by Bester (1985), represents a downside risk decision: there is a low probability of the ‘bad payoff,’ i.e., of losing the collateral.

Additionally, the empirical research of Bajtelsmit et al. (1999) found women more risk averse than men in financial decisions on pension allocation. Jianakoplos and Bernasek (1998) and Halko et al. (2012) found women had less risky asset portfolios than men, and Barsky et al. (1997) showed that women reported lower willingness to accept financial risk.

Experimental studies have also found that women are more risk averse than men when making financial decisions, as the literature reviews of Charness and Gneezy (2012), Croson and Gneezy (2009), and Eckel and Grossman (2008) showed.

The theoretical paper by Smart (2000) demonstrates that the addition of the customer’s degree of risk aversion can change the self-selection equilibrium of Bester (1985), resulting in different risk classes pooled at a single contract. Specifically, risk averse low-risk borrowers may not be willing to accept higher collateral to self-select.

The collateral choice is closely connected to the degree of risk aversion, as shown by Cohen and Einav (2007), Barseghyan et al. (2011) and Shih and Ke (2014). The higher the risk aversion the lower the willingness to accept higher collateral. Low collateral exposes individuals to a lower risk of a greater loss (the collateral) by paying a higher contract price (interest rate).

The goal of this paper is to experimentally test the consequences that women’s pattern of behavior toward risk carry over into the self-selection mechanism with collateral. Laboratory economic experiments are exceptionally well suited to test, under controlled conditions, the gender differences in financial decisions.

This is an important topic with implications on entrepreneurship opportunities. If women do not accept higher collateral to self-select, they will be wrongly classified by banks as high-risk borrowers, leading to potential women credit rejections and creating an institutional barrier for female entrepreneurship.

The scarcity of women engaged in entrepreneurial activities is well documented. The research of Coleman (2000), Kim (2007), Coleman and Robb (2012), Koellinger et al. (2013), and Anggadwita et al. (2021) showed that women still own significantly fewer business than men worldwide. There is substantial scope for further research on the reasons behind this gender gap in entrepreneurial propensity.

Financial limitations have been found in previous research. Mijid and Bernasek (2013) reported that women initiating ventures have less access to financial resources. Alsos et al. (2006) found that women entrepreneurs tend to start ventures with lower amounts of initial funding; and Kanze et al. (2018) showed that women are less likely to attract external funds.

It is important to note that Eddleston et al. (2016) found that when women entrepreneurs obtain loans, they are more likely to acquire smaller loans, and Wu and Chua (2012) showed that loans granted to women had significantly higher interest rates.

Among the underlying causes, subjective factors have been found. Koellinger et al. (2013) and Wagner (2004), using data from the Global Entrepreneurship Monitor (GEM) project, showed that subjective perceptions as self-confidence and fear of failure are key to explain the gender gap in entrepreneurship. Both perceptions, self-confidence and fear of failure, are closely connected to the individual’s degree of financial risk aversion.

Comeig and Lurbe (2018), in a review of economic laboratory experiments which analyzes men’s and women’s self-confidence and fear of failure, showed that correcting such subjective perceptions requires awareness and changing cultural factors.

Therefore, in this paper we contribute to raising awareness about the systematic gender differences in credit self-selection and screening, in contracts with collateral. Not taking into account this gender difference can lead to financial limitations toward women, damaging female entrepreneurship.

There are only a few experimental papers on screening. Most of them have focused on insurance and labor markets and on the principal’s behavior, not on the self-selection mechanism (e. g., Shapira and Venezia 1999; Posey and Yavas 2007; Kübler et al. 2008). On the other hand, the scarce experimental literature that has analyzed this self-selection mechanism in credit markets has focused on the effects of moral hazard (Capra et al. 2009) and on the framing effects of incentive-compatible contracts (Bediou et al. 2013). This paper’s approach is different; it studies the effect of gender on contract choices.

Based on previous literature results and by presenting ad hoc incentive-compatible contracts à la Bester (1985), we test the following hypotheses:

H1

Incentive-compatible contracts with collateral screen men of different risk levels but fail to screen women by risk level.

H2

There is a gender difference when applicants face high collateral loans.

3 Method

In order to study if women are more risk averse than men in this financial decision-making setting and, therefore, women do not accept higher collateral to self-select, we design and run an economic experiment based on Bester (1985) incentive-compatible contracts with collateral.

The experiment consists on a sequence of two phases: (i) we first measure individual risk attitudes and also individual ambiguity attitudes within undergraduate students of three different European countries and (ii) we then offer those subjects menus of two incentive-compatible contracts to study self-selection.

The experiment has been run in north, central, and south Europe. The goal was to control for possible cultural differences among Central Europe (Switzerland), Atlantic (UK), and Mediterranean (Spain) European countries.

At the end of the experiment, subjects answered a sociodemographic questionnaire to control for differences in technical skills and wealth between men and women. The answers showed no significant differences in these two factors between men and women.

3.1 Test on individual risk and ambiguity attitudes

To measure attitudes toward risk and ambiguity, subjects are confronted with nine lottery pairs in 2 different conditions: risk and ambiguity. The lottery pairs follow Blavatskyy (2009) test on risk and ambiguity attitudes, based on Holt and Laury (2002) test on risk attitudes. We use three different stimuli (cards, bars, and gambles). Each lottery is presented twice to each subject in order to control for the effect side (left/right) and colors. Figure 1 shows the screen’s design.

Fig. 1
figure 1

Test on individual risk attitudes and individual ambiguity attitudes

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3.2 Test on self-selection mechanism

To study the women’s patterns of behavior in the self-selection mechanism, we use five incentive-compatible contract menus (with collateral) to induce subjects to disclose their private information. We follow the experimental design and menus presentation of Bediou et al. (2013), who used the contract menus originally designed by Capra et al. (2009). This contract design is based on the Bester’s (1985) principal agent game of credit screening.

Table 1 shows the 5 menus of contracts offered to the subjects and Table 2 presents the expected returns on each contract for both, low-risk individuals and high-risk individuals.

Table 1 Pairs of offered contracts
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Table 2 Individuals expected returns (ER) by contract
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In the experiment, subjects choose between the two contracts (and a safe option). All subjects had the safer project (were low-risk borrowers) during ten rounds and had the riskier project (were high-risk borrowers) the other ten rounds. The safer project, s, has 90% chance of success, and the risky project, r, has 50% chance of success. Appendix presents the instructions used in this experiment.

Each individual started each round with a wealth of 300 units. Each subject chose one or none of the two offered contracts in each round. The subjects who did not choose any contract received a return of 30 monetary units in that round. Under Expected Utility, as in Bester’s (1985) model, the individual-expected payoffs were as follows:

$$E_{{{\text{Payoff}}}} \left( {\tilde{O}_{s} } \right) = 0.9{\mkern 1mu} \left( {300 + 600 - P_{j} } \right) + 0.1{\mkern 1mu} \left( {300 + 0 - D_{j} } \right)$$
(1)
$$E_{{{\text{Payoff}}}} \left( {\tilde{O}_{r} } \right) = 0.5{\mkern 1mu} \left( {300 + 1080 - P_{j} } \right) + {\mkern 1mu} 0.5{\mkern 1mu} \left( {300 + 0 - D_{j} } \right).$$
(2)

Thus, in each of the rounds a pair of theoretically incentive-compatible contracts (gr, gs) was offered: \(\tilde{O}_{r} \left( {g_{r} } \right) \ge \tilde{O}_{r} \left( {g_{s} } \right){\mkern 1mu} {\text{and}}{\mkern 1mu} \;\tilde{O}_{s} \left( {g_{s} } \right) \ge \;\tilde{O}_{s} \left( {g_{r} } \right)\).

The within subjects design allows us to control for individual differences in personality or risk attitude. Half of the subjects played with the riskier project first to control for order effects.

Therefore, the design of the experiment controls for the treatment order and the presentation (right/left; blue/yellow colors). Also, by presenting two times the same contract, the design allows for indifference (i.e., an indifferent participant may choose contract r once and contract s once).

The 143 subjects of the experiment were students from the University of Geneva, Switzerland (23 men, 24 women), the University of Valencia, Spain (24 men, 24 women), and the University of East Anglia, UK (24 men, 24 women). They were recruited from various courses and grades using flyers. The individuals read the instructions and we answered their questions. During the experiment, the subjects received no feedback and were not allowed to communicate with the rest of the participants. At the end of the experiment, they received their earnings (the average payment was 15 Euros). Subjects were paid one round drawn at random per treatment in the first phase (6 rounds in total). In the second phase, subjects were paid two rounds drawn at random: one from the low risk and one from the high-risk project. Given that the experiment was run in different countries with different currencies, British Pound, Swiss Franc, and Euro, we used ECUs as experimental monetary units, to homogenize the three different currencies during the experiment.

Each session lasted approximately one hour and 15 min and was run at: (i) the University of Geneva, either at the laboratory of the Swiss Center for Affective Sciences or at the laboratory of the Faculty of Psychology; (ii) the University of Valencia, at the Laboratory for Research in Experimental Economics (LINEEX); and (iii) the Centre for Behavioral and Experimental Social Science at the University of East Anglia. The experiment was run in different time periods in each country.

4 Results

4.1 Attitudes toward risk and ambiguity

Figure 2 shows that most of the subjects (represented by dots) were concentrated in the fourth quadrant: risk and ambiguity averse individuals. The proportion of risk averse individuals was higher than the proportion of risk neutral or risk-seeking individuals. Similarly, the proportion of ambiguity averse individuals was higher than the proportion of ambiguity neutral or ambiguity-seeking individuals.

Fig. 2
figure 2

Individual’s risk attitudes and ambiguity attitudes: overall and by country

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This pattern is found in each of the three countries and overall.

Regarding the gender attitudes, Fig. 2 shows that women were, overall, more concentrated in the fourth quadrant than men. The results of the Mann–Whitney test showed significant gender differences in risk attitudes but not in ambiguity attitudes (p = 0.0159 and p = 0.9586, respectively). Thus, gender differences in risk attitudes were found, being women more risk averse than men.

When studying this effect by countries using a Kruskal–Wallis test with all countries, women’s risk attitudes did not differ by country (p = 0.1856). There were no significant differences in men’s attitudes toward risk by country either (p = 0.5648). So the overall result of significant gender differences in risk attitudes, being women more risk averse than men, applies.

However, this result does not correlate to ambiguity attitudes. Using a spearman correlation test, ambiguity and risky choices were independent in both genders (p = 0.1897 for women and p = 0.3041 for men).

By country, using a Mann–Whitney test, Swiss men were found to be more ambiguity averse than Spanish and British men (p = 0.0013 and p = 0.0529, respectively).

In conclusion, after analyzing the results on attitudes toward risk from the first part of the experiment, by country and overall, significant gender differences in risk attitudes were found; being women more risk averse than men.

It is important to note that, as the theoretical work of Smart (2000) pointed out, with systematic gender differences in risk attitudes, different risk classes (low risk and high risk) may be pooled at a single contract in equilibrium, and incentive-compatible contracts with collateral may fail to disclose women’s private information.

In order to prepare the previously analyzed data on risk and ambiguity decisions, given that the attitudes tests were run with three different stimuli (cards, bars, and gambles) and repeated twice to control the left/right effect, we used the average switch point from safer (unambiguous) to risk (ambiguous) option.

To do so, we calculated if there was a Unique Switching Point (USP) for each subject and condition. This was done by comparing the lowest (highest) probability at which a subject chooses the safe (unambiguous) option, with the highest (lowest) probability at which each subject chooses the risky (ambiguous) option. If the two values did not overlap, then the subject had a USP, which means that she/he was choice consistent. Otherwise, the subject’s choices were considered inconsistent.

We created this average only when subjects selected a unique switching point (subjects faced decision problems in a random order and, therefore, they were not restricted to select a unique switching point). Using a Fisher’s exact test, there were no differences between stimulus and side effect (given the high number of tests, they are available upon request).

Table 3 shows the percentage of women and men who had always a USP in all tests, some USP in the three different stimulus, and were inconsistent in all of them.

Table 3 Percentage of consistent subjects in risk and ambiguity choices distinguishing between gender
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4.2 Self-selection test

The results of the experiment run in the three countries are summarized in Fig. 3 and Table 4. Figure 3 shows the histograms of the overall results by gender and project type. Most of the men with the safer project chose the high collateral (HC) contract, 67.88%, whereas just the 49.72% of women with safer project chose the high collateral contract. Table 4 confirms that low-risk women (women with safer project) did not self-select by choosing the contract with high collateral (p = 0.3056).

Fig. 3
figure 3

Histogram by gender and project risk level

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Table 4 Test statistics by gender and project
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Results did not show significant differences between the choice of the low and the high collateral contract in women with the safer project, the one banks want to grant credit. Therefore, low-risk women did not self-select by choosing the contract theoretically designed for low-risk borrowers and women’s screening failed to occur. This result supports H1: Incentive-compatible contracts with collateral screen men of different risk levels but fail to screen women by risk level.

As Mann–Whitney tests from the second part of Table 4 show, there are no gender differences in choices when subjects have the riskier project (p = 0.1746 for low collateral contracts, and p = 0.8503 for high collateral contracts).

However, there are significant gender differences in choices when subjects have the safer project (p = 0.0121 for low collateral contracts, and p = 0.0013 for high collateral contracts). Note that borrowers with a safer project, i.e., low probability of failure, are the target borrowers for the banks and other credit service business, the borrowers that may get credit. If women do not self-select in this case, by choosing the high collateral contract they face a barrier in obtaining funds.

Figure 4 and Table 5 show the results by country. As can be seen in Table 5, there were not significant differences across countries in the choices of the high and low collateral contract. In each country men disclosed its private information with this self-selection mechanism, whereas low-risk women did not.

Fig. 4
figure 4

Histograms by country, gender, and project risk level

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Table 5 Test statistics between country, gender, and project risk level
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Using Mann–Whitney test for each country pairs, we found the same results as Kruskal–Wallis test with all countries.

Additionally, we ran logistic models to confirm that self-selection was influenced by gender and not by country, as descriptive statistics showed. Table 6 displays the results of the logistic analysis. The self-selection option equals 1 if the subject chose low collateral with the riskier project and high collateral with the safer project. In the overall model, safer project variable indicated that having the safer project decreased the probability of choosing the best option (the option designed by the theoretical model to screen low risk from high-risk borrowers). This effect came from the women’s choices. Low-risk women did not self-select by choosing the contract with high collateral. This was shown in the variable interactions: logistic models ran with the interaction safer project and ambiguity and safer project and risk attitudes. Both attitudes significantly interacted with the safer project (Model 1); they also interacted with gender (Model 2).

Table 6 Logit models
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Model 1 shows that interaction safer project–ambiguity attitude acted in opposite direction to safer project–risk attitude interaction: The higher the risk aversion the lower the probability of choosing the contract defined by the theoretical model.

However, the higher the ambiguity aversion, the higher probability of choosing the contract defined by the theoretical model.

Model 2 shows this effect specifically in women choices.

In conclusion, results showed that the probability of choosing the theoretical self-selection option depended on gender and supports H1: Incentive-compatible contracts with collateral screen men of different risk levels but fail to screen women by risk level. Also, the H2 is confirmed: Gender differences appeared when subjects were expected to choose high collateral (customers with safer project). There is a gender difference when applicants face high collateral loans.

The overall logit model, from Table 6, also shows that self-selection did not depend on the country.

In summary, the results of the experiment showed

  1. 1.

    Men borrowers self-selected but women borrowers did not self-select following the theoretical model designed for a uniform risk attitude: Theoretical incentive-compatible contracts with collateral used to induce borrowers to disclose their private information fail to disclose women’s private information.

  2. 2.

    Gender differences arose when borrowers faced low-risk projects: 90% success probability and 10% failure probability. When subjects faced high-risk projects: 50% success probability, no gender differences in behavior were found.

At this point it is important to highlight that subjects with safer projects were equally rational deciding high collateral or low collateral contract. Given that the high collateral contract had a higher variance, decisions depended on the risk-taking behavior.

5 Concluding remarks and discussion

We have conducted an experiment to study the extent to which the women’s pattern of behavior toward risk carry over into the theoretical and widely applied self-selection mechanism with collateral, a problem which reduces women’s access to funds. This problem affects female entrepreneurs negatively which, in turn, has important economic and policy implications.

Extant theories on credit screening assume that borrowers’ preferences among different combinations of price and collateral systematically depend on the risk level of their projects. The contract with high collateral and low interest rate is the one theoretically chosen by the low-risk borrowers. Banks, in turn, extract information from this borrower’s choice and grant credit mainly to those who chose high collateral (and low interest rate).

However, these models so far have not addressed an important question for such settings: Does the women’s risk-taking behavior interfere with the self-selection mechanism? Results from this research show that women avoid the high collateral contract. In this way, gender does affect the contract choice and interferes with the screening mechanism. This result suggests gender differences in self-selection that can negatively affect women in price and access to credit and entrepreneurship.

The results of this experiment clearly indicate that men and women differ in their choices under this credit screening mechanism. Consequently, incentive-compatible contracts with collateral fail to disclose women’s private information: Low-risk women borrowers do not self-select as the good borrowers they really are, due to the design of the generally accepted credit screening mechanism.

This research contributes to raising awareness about the systematic gender difference in credit self-selection and screening, in contracts with collateral. Credit service businesses, such as banks, along with women themselves, and society at large, should pay attention to this bias in order to reduce discrimination and unbalanced entrepreneurship opportunities.

Failure to take into account this gender difference can create financial constraints for women, undermining female progress and entrepreneurship.

5.1 Academic and practitioner’s implications

On one hand, given the results of this paper and other experimental and empirical literature showing gender differences in risk-taking behavior, academic theoretical models should start incorporating such differences. When constructing an economic model, the first step is to depict how economic agents cope with uncertainty (risk, ambiguity, or both) and then, based on those agent’s uncertainty preferences, the equilibrium interactions are reached.

It is important to note that nowadays algorithms are becoming ubiquitous in credit markets. Those algorithms are based on theoretical models and grow from experience. Algorithms perform the first screening in granting or denying credit. If the theoretical model is already leaving behind a big portion of the population (women), algorithms will grow with only half of the experience and may reinforce the barriers to female progress and entrepreneurship.

On the other hand, credit service businesses, such as banks, should pay attention to this bias. Essentially, the women’s reluctance to accept high collateral generates an adverse selection problem for the bank. The women wrongly classified here as high-risk borrowers are particularly risk averse, so they may also be the best borrowers for the bank, low-risk borrowers. Therefore, some human factor should be introduced in the first screening of borrowers in order to perceive these gender biases and classify low-risk woman borrowers as low-risk borrowers, regardless of their collateral choice.

Women, in turn, have to be aware of the consequences and limitations this lack of self-selection entails. Correcting such biases requires awareness, experience, and changing cultural factors that may be connected to social experiences.