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Fintech, Credit Market Competition, and Bank Asset Quality

Abstract

This study explores bank screening incentives under credit market competition between traditional banks and a Fintech startup. The bank screening incentives increase with the cost of the Fintech startup’s screening technology, decrease with the performance of that technology, and increase with the cost of entrepreneurs’ conveying information to the Fintech startup. However, when the preparation cost of entrepreneurs applying to the banks for loans falls with Fintech, the bank screening incentives are eroded; while when the bank screening cost decreases with Fintech, those incentives are enhanced. We also discuss the role of capital regulation and several extensions for robustness.

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Notes

  1. Among these applications, the digitalization of the payment and settlement system decreases the cost of transactions and financial services and products (Parlour et al. 2016; Vives 2017; Fuster et al. 2019). Artificial intelligence and big data may be applied to reduce information asymmetry between investors and financial intermediaries and the conflict of interest that plagues the financial industry (Morse 2015; Philippon 2016; Jakšič and Marinč 2017; Vives 2017; He et al. 2017; Fuster et al. 2019). Moreover, peer-to-peer lending platforms increase the financing options for consumers and entrepreneurs of small and medium enterprises (Braggion et al. 2017; Martinez-Miera and Schliephake 2017; Buchak et al. 2018; Jagtiani and Lemieux 2018; Tang 2019). Other related studies are Philippon (2016), Boot (2016), and Vives (2017).

  2. There is a growing body of literature that explores banks’ incentives for risk-taking under competition between heterogeneous lenders. See De Fraja (2009), Saha and Sensarma (2013), Bose et al. (2014), and Gormley (2014).

  3. Loan screening and monitoring services provided by banks are supported by the empirical literature. For instance, Lee and Sharpe (2009) use an ex-ante proxy for bank screening and monitoring that was developed by Coleman et al. (2006), salary expenses on the banks’ stuff to explore the effects of bank screening and monitoring on borrowers’ value. They find a statistically significant and positive relationship between that proxy and the borrower’s standardized cumulative abnormal return, which is consistent with the result that bank’s loan screening and monitoring do add value to the borrower.

  4. When the Fintech startup persistently collects and analyzes data about the entrepreneurs and their projects, it can efficiently screen the applications ex-ante. This is consistent with the argument by Agrawal et al. (2014), Morse (2015), Claessens et al. (2018), Balyuk and Davydenko (2018), Thakor (2020), and Sutherland (2020).

  5. Fuster et al. (2019) emphasize the role of information technology in the lending process of Fintech startups. Since technological progress is not easily controlled by Fintech startups, we assume that their screening technology is sticky. Furthermore, the screening information analyzed by the Fintech startup is gathered from social media, E-commerce transactions, and activities on the internet that are largely ignored by traditional banks. The screening technology is based on artificial intelligence and big data from progress in information technology that differ from loan officers’ judgements in traditional banks (Morse 2015; Vives 2017; Martinez-Miera and Schliephake 2017; Jakšič and Marinč 2017; Buchak et al. 2018; Merton and Thakor 2018).

  6. See discussion of Philippon (2016), Vives (2017), and Jakšič and Marinč (2017).

  7. For both the ease of exposition and the concentration on the effects from advances in Fintech on the banks’ screening incentives, we do not add a layer of monitoring that is an important rationale for the existence of banks (Diamond 1984), and whose primary function is to increase the success probability of the banks’ assets (Holmström and Tiróle 1997; Boot and Thakor 2000; Allen et al. 2011; Dell’Ariccia et al. 2014).

  8. This functional form of the screening cost is consistent with Vanasco (2017) and Martinez-Miera and Repullo (2019). Furthermore, a larger c may mean more severe information asymmetry between the banks and the entrepreneurs (Cordella et al. 2018), and thus the effort by the banks to enhance the probability of the gG group is more costly.

  9. This study emphasizes how credit market competition between the Fintech startup and the traditional banks affects the banks’ screening incentives. Thus, our model abstracts from the optimization on the liability side of the banks and assumes that depositors are protected by deposit insurance (Hellmann et al. 2000; Repullo 2004; Gomez and Ponce 2014). Some studies have explored the role of deposit insurance under the competition in the deposit market; see Matutes and Vives (2000), Cordella and Yeyati (2002), and Allen and Gale (2004).

  10. Besides referring to the physical cost of travelling, the transportation cost in the spatial model of Salop (1979) does not only represent utility losses caused by differences between the ideal products consumers want and the actual products banks provide (Inderst 2013; Pennacchi 2019), but also the communication cost induced by information asymmetry between borrowers and banks (Hauswald and Marquez 2006; Martinez-Miera and Schliephake 2017).

  11. Another reason why the entrepreneurs do not borrow from multiple lenders is that the preparation cost is high and being rejected entails entrepreneurs’ disutility so that the entrepreneurs do not apply for loans to other lenders when rejected.

  12. Note that Fig. 1 shows that the following loan demand an individual bank faces is only valid if x involves only the entrepreneurs less than half the distance to the nearest competitor banks, 1/(2N).

  13. For a more detailed exposition on the differences between the idea of “price in equilibrium” and that of “price at the margin”, please refer to Cordella et al. (2018).

  14. The reason why we do not discuss the stage at which the traditional banks compete for the screening technology of the Fintech startup is that it involves the issue of what kind of contract the Fintech startup uses when selling its screening technology. Does the Fintech startup outright sell its screening technology, or just license it? This issue is beyond the scope of this article and we leave it to future research.

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Correspondence to Ping-Lun Tseng.

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We are deeply grateful to the Editor Nagpurnanand R. Prabhala and two anonymous referees for their valuable suggestions. Jonathan Moore is appreciated for his editorial assistance. All remaining errors are ours.

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Appendix

Appendix

Derivation of the equilibrium in Section 3.2

From Eq. (5), we can obtain the first-order conditions with respect to bank i’s screening effort αi and loan rate ri:

$$ \begin{aligned} & \frac{\partial {\Pi}_{i}}{\partial \alpha_{i}} = (r_{i} - c \widehat{\alpha_{i}} ) L_{i}^{\scriptscriptstyle D} =0, \end{aligned} $$
(30)
$$ \begin{aligned} & \frac{\partial {\Pi}_{i}}{\partial r_{i}} & = (\phi_{b} + \alpha_{i}) \left\{ 2 \left[\frac{t_{f}}{t} + \frac{(\phi_{b} + {\alpha^{e}_{i}}) (R - \widehat{r_{i}}) - (\phi_{f} + {\upbeta}^{e}) (R - r_{f})}{t \gamma } \right] \right\} \\ & & + \left[ (\phi_{b} + \alpha_{i}) \widehat{r_{i}} - (\phi_{b} + \psi_{b})r_{\scriptscriptstyle D}- \frac{1}{2} c \alpha_{i}^2 \right] \left[ \frac{- 2 (\phi_{b} + {\alpha_{i}^{e}}) }{ t \gamma}\right] =0. \end{aligned} $$
(31)

Some calculation leads to \(\partial ^{2} {\Pi }_{i} \big / \partial \alpha _{i}^{2} = (- c) L_{i}^{\scriptscriptstyle D} < 0\) and \(\partial ^{2} {\Pi }_{i} \big / \partial r_{i}^{2} = \big [(\phi _{b} + \alpha _{i})(2) (\phi _{b} + {\alpha _{i}^{e}}) (-1) \big ] \big /t \gamma + \big [(\phi _{b} + \alpha _{i}) (- 2)(\phi _{b} + {\alpha _{i}^{e}})\big ] \big / t \gamma < 0\). For simplicity, we further assume for the sufficient condition to hold that parameters are such that \(\left (\partial ^{2} {\Pi }_{i} \big / \partial \alpha _{i}^{2} \right ) \times \left (\partial ^{2} {\Pi }_{i} \big / \partial r_{i}^{2} \right ) - \left (\partial ^{2} {\Pi }_{i} \big / \partial \alpha _{i} \partial r_{i} \right )^{2} >0\).

Similarly, taking the first-order condition of Eq. (6) with respect to the Fintech startup’s loan rate rf yields

$$ \begin{aligned} & \frac{\partial {\Pi}_{f}}{\partial r_{f}} & = (\phi_{f} + \upbeta) N \left\{ \frac{1}{N} - 2 \left[\frac{t_{f}}{t} + \frac{(\phi_{b} + {\alpha^{e}_{i}}) (R - r_{i}) - (\phi_{f} + {\upbeta}^{e}) (R - \widehat{r_{f}})}{t \gamma } \right] \right\} \\ & & + \Big[(\phi_{f} + \upbeta) \widehat{r_{f}} - (\phi_{f} + \psi_{f}) r_{\scriptscriptstyle K} - \mu_{f} \Big] N \left\{ - 2 \left[ \frac{ - (\phi_{f} + {\upbeta}^{e}) (-1)}{t \gamma} \right] \right\} =0. \end{aligned} $$
(32)

Simple calculation gives us \(\partial ^{2} {\Pi }_{f} \big / \partial r_{f}^{2} = \big [ (\phi _{f} + \upbeta ) (2) (\phi _{f} + {\upbeta }^{e}) (-1) \big ] \big / t \gamma + (\phi _{f} + \upbeta ) \left \{ - 2 \big [ - (\phi _{f} + {\upbeta }^{e}) (-1) \big / t \gamma \big ] \right \} <0\), which confirms the sufficient condition for rf. We then impose the rational expectations and substitute \({\alpha _{i}^{e}} = \alpha _{i}\) and βe =β into the first-order conditions of (31) and (32). Rewriting them yields Eqs. (7), (8), and (9).

We next impose symmetry on (7), (8), and (9) and solve for the banks’ screening effort α and loan rate r and the Fintech startup’s loan rate \(r_{f}^{*}\), which are

$$ \alpha^{*} = \frac{1}{4} \left( \frac{-3 N \phi_{b} c + N R+ {\Phi} }{N c} \right), $$
(33)
$$ r^{*} = \frac{1}{4} \left( \frac{-3 N \phi_{b} c + N R + {\Phi}}{N} \right), $$
(34)
$$ r_{f}^{*} {=} \frac{1}{16} \frac{\left[ \begin{aligned} & 4 \phi_{f} N R c + 4 \upbeta N R c + 8 N r_{\scriptscriptstyle D} \psi_{b} c - 4 N t_{f} \gamma c + 6 t \gamma c + 12 r_{\scriptscriptstyle K} N \phi_{f} c - 2 N \phi_{b} R c \\ & + 8 N r_{\scriptscriptstyle D} \phi_{b} c + 12 r_{\scriptscriptstyle K} N \psi_{f} c + 12 \mu_{f} N c + 3 N c^{2} {\phi_{b}^{2}} -c \phi_{b} {\Phi} - N R^{2} - R {\Phi} \end{aligned} \right] }{(\phi_{f} + \upbeta) N c}, $$
(35)

where

$$ {\Phi} \equiv \sqrt{ \begin{aligned} & N (9 N c^{2} {\phi_{b}^{2}} + 2 N \phi_{b} R c + N R^{2} - 8 \upbeta N R c + 16 N r_{\scriptscriptstyle D} \psi_{b} c + 8 N t_{f} \gamma c \\ & - 8 \phi_{f} N R c + 8 r_{\scriptscriptstyle K} N \phi_{f} c + 16 N r_{\scriptscriptstyle D} \phi_{b} c+ 8 r_{\scriptscriptstyle K} N \psi_{f} c + 8 \mu_{f} N c + 4 t \gamma c). \end{aligned} } $$

For the existence of an equilibrium, we assume that the term under the square root sign of Φ is greater than 0, that is

$$ \begin{aligned} & N (9 N c^{2} {\phi_{b}^{2}} + 2 N \phi_{b} R c + N R^{2} - 8 \upbeta N R c + 16 N r_{\scriptscriptstyle D} \psi_{b} c + 8 N t_{f} \gamma c \\ & \qquad - 8 \phi_{f} N R c + 8 r_{\scriptscriptstyle K} N \phi_{f} c + 16 N r_{\scriptscriptstyle D} \phi_{b} c + 8 r_{\scriptscriptstyle K} N \psi_{f} c + 8 \mu_{f} N c + 4 t \gamma c) >0. \end{aligned} $$

The similar assumption is made and discussed in Allen et al. (2011) and Cordella et al. (2018). Rewriting gives us

$$ N(R + \phi_{b} c)^{2} + 8 N c \Bigg\{ \bigg[-R(\phi_{f} + \upbeta) \bigg] + \bigg[ r_{\scriptscriptstyle K} (\phi_{f} + \psi_{f}) + 2 r_{\scriptscriptstyle D} (\phi_{b} + \psi_{b}) + (t_{f} \gamma + \mu_{f}) + {\phi_{b}^{2}} c + \frac{1}{2}\frac{t \gamma}{N} \bigg] \Bigg\} >0. $$

In other word, when the improved probability of loans granted to good entrepreneurs of the Fintech startup’s screening technology, ϕf +β, and the number of the banks N are not too high, and when the funding costs of the Fintech startup and the banks, rK(ϕf + ψf) and rD(ϕb + ψb), the preparation cost of entrepreneurs applying for a loan to the lenders, t and tf, the screening cost of the Fintech startup μf, the efficiency of the banks’ screening technology, ϕb and c, the proportion of good entrepreneurs γ, and the return of the good entrepreneur’s project R are not too low, it is more likely that our assumption for the existence of the equilibrium holds. Moreover, for the interior solution we are interested in, we further assume that the parameters are such that 0 < α < 1, rD < r < R, and \(r_{\scriptscriptstyle K} < r_{f}^{*} < R\).

Proof of Proposition 1

From Eq. (33), some calculation yields

$$ \frac{\partial \alpha^{*}}{\partial \mu_{f}} = \frac{1}{4 N c} (8 N^{2} c) \frac{1}{2} \frac{1}{\Phi} = \frac{N}{\Phi} >0 $$

and

$$ \frac{\partial \alpha^{*}}{\partial \upbeta} = \frac{1}{4 N c} \big(- 8 N^{2} R c \big) \left( \frac{1}{2} \right) \frac{1}{\Phi} = \frac{-N R}{\Phi} < 0. $$

Proof of Proposition 2

From Eq. (33), we can obtain

$$ \frac{\partial \alpha^{*}}{\partial t_{f}} = \frac{1}{4 N c} \big(8 N^{2} \gamma c \big) \left( \frac{1}{2} \right) \frac{1}{\Phi} = \frac{N \gamma}{\Phi} > 0 $$

and

$$ \frac{\partial \alpha^{*}}{\partial t} = \frac{1}{4 N c} \big(4 N \gamma c \big) \left( \frac{1}{2} \right) \left( \frac{1}{\Phi} \right) =\frac{\gamma}{2} \left( \frac{1}{\Phi} \right) >0. $$

Proof of Proposition 3

Taking the partial derivative of the banks’ optimal level of screening effort α with respect to the transformation coefficient c yields

$$ \begin{aligned} & \frac{\partial \alpha^{*}}{\partial c} = \frac{1}{4} \frac{ \left\{ \begin{aligned} & - N \phi_{b} R c - 8 N r_{\scriptscriptstyle D} \psi_{b} c - 8 N r_{\scriptscriptstyle D} \phi_{b} c - 4 r_{\scriptscriptstyle K} N \psi_{f} c + 4 \upbeta N R c \\ & + 4 \phi_{f} N R c - 4 N t_{f} \gamma c - 4 r_{\scriptscriptstyle K} N \phi_{f} c - 4 \mu_{f} N c - 2 t \gamma c - R {\Phi} - N R^{2} \end{aligned} \right\}}{c^{2} {\Phi}}. \end{aligned} $$

The sign of α/c depends on that of the numerator.

Since it is assumed that the parameters are such that 0 < α < 1, we have

$$ \alpha^{*} = \frac{1}{4} \left( \frac{-3 N \phi_{b} c + N R+ {\Phi} }{N c} \right) > 0. $$

By assumption,

$$ (N R+ {\Phi})^{2} > (3 N \phi_{b} c)^{2} $$
(36)

holds. Rearranging Eq. (36), we obtain

$$ \begin{aligned} & -2 N (- N \phi_{b} R c - 8 N r_{\scriptscriptstyle D} \psi_{b} c - 8 N r_{\scriptscriptstyle D} \phi_{b} c - 4 r_{\scriptscriptstyle K} N \psi_{f} c + 4 \upbeta N R c \\ & \qquad + 4 \phi_{f} N R c - 4 N t_{f} \gamma c - 4 r_{\scriptscriptstyle K} N \phi_{f} c - 4 \mu_{f} N c - 2 t \gamma c - R {\Phi} - N R^{2}) >0, \end{aligned} $$

and

$$ \begin{aligned} & - N \phi_{b} R c - 8 N r_{\scriptscriptstyle D} \psi_{b} c - 8 N r_{\scriptscriptstyle D} \phi_{b} c - 4 r_{\scriptscriptstyle K} N \psi_{f} c + 4 \upbeta N R c \\ & \qquad + 4 \phi_{f} N R c - 4 N t_{f} \gamma c - 4 r_{\scriptscriptstyle K} N \phi_{f} c - 4 \mu_{f} N c - 2 t \gamma c - R {\Phi} - N R^{2} <0. \end{aligned} $$

Consequently, we have q/c < 0. □

Proof of Proposition 4

From Eq. (33) and further calculations, we obtain

$$ \frac{\partial \alpha^{*}}{\partial r_{\scriptscriptstyle K}} = \frac{1}{4 N c} \Big[ 8 N^{2} (\phi_{f} + \psi_{f}) c \Big] \left( \frac{1}{2} \right) \left( \frac{1}{\Phi} \right) =\frac{N (\phi_{f} + \psi_{f})}{\Phi} > 0. $$

Derivation of the equilibrium in Section 4

We solve the model as in Section 3.2. The first-order conditions of the bank i’s maximization problem (11) with respect to the screening effort and the loan rate can be written as:

$$ \begin{aligned} & \frac{\partial {{\Pi}_{i}^{k}}}{\partial \alpha_{i}} = \left\{ r_{i} - c \widetilde{\alpha_{i}} \right\} L_{i}^{\scriptscriptstyle D} =0, \end{aligned} $$
(37)
$$ \begin{aligned} & \frac{\partial {{\Pi}_{i}^{k}}}{\partial r_{i}} = (\phi_{b} + \alpha_{i}) \left\{ 2 \left[ \frac{t_{f}}{t} + \frac{(\phi_{b} + \alpha_{i}^{e}) (R - \widetilde{r_{i}}) - (\phi_{f} + {\upbeta}^{e}) (R - r_{f})}{t \gamma} \right] \right\} \\ & \quad \qquad + \left\{ (\phi_{b} + \alpha_{i}) \widetilde{r_{i}} - \big[(\phi_{b} + \alpha_{i}) + (\psi_{b} - \alpha_{i}) \big] \big[(1-k) r_{\scriptscriptstyle D} + k r_{\scriptscriptstyle K} \big] - \frac{1}{2} c {\alpha_{i}^{2}} \right\} \left[ \frac{- 2 (\phi_{b} + \alpha_{i}^{e}) }{t \gamma}\right] \\ & \quad \qquad =0. \end{aligned} $$
(38)

The first-order condition of the Fintech startup’s maximization problem (6) with respect to it loan rate can be written as:

$$ \begin{aligned} & \frac{\partial {\Pi}_{\scriptscriptstyle F}}{\partial r_{f}} & = (\phi_{f} + \upbeta) N \left\{ \frac{1}{N} - 2 \left[\frac{t_{f}}{t} + \frac{(\phi_{b} + {\alpha^{e}_{i}}) (R - r_{i}) - (\phi_{f} + {\upbeta}^{e}) (R - \widetilde{r_{f}})}{t \gamma } \right] \right\} \\ & & + \Big[(\phi_{f} + \upbeta) \widetilde{r_{f}} - (\phi_{f} + \psi_{f}) r_{\scriptscriptstyle K} - \mu_{f} \Big] N \left\{ - 2 \left[ \frac{ - (\phi_{f} + {\upbeta}^{e}) (-1)}{t \gamma} \right] \right\} =0. \end{aligned} $$
(39)

Simple calculations reveal that the second order conditions hold for the bank i and the Fintech startup. Imposing rational expectations, \({\alpha _{i}^{e}} = \alpha _{i}\), βe =β, on the first order conditions (37), (38), and (39) yields Eqs. (12), (13), and (14).

We then impose the symmetry on the conditions and solve for the equilibrium screening effort α∗∗ and loan rate r∗∗ of the banks and the equilibrium loan rate set by the Fintech startup \(r_{f}^{**}\), which can be written as:

$$ \alpha^{**} = \frac{1}{4} \left( \frac{-3 N \phi_{b} c + N R+ {\Omega} }{N c} \right), $$
(40)
$$ r^{**} = \frac{1}{4} \left( \frac{-3 N \phi_{b} c + N R + {\Omega}}{N} \right), $$
(41)
$$ r_{f}^{**} = \frac{1}{16} \frac{\left[ \begin{aligned} & 4 \phi_{f} N R c + 4 \upbeta N R c + 8 N r_{\scriptscriptstyle D} \psi_{b} c - 4 N t_{f} \gamma c + 6 t \gamma c + 12 r_{\scriptscriptstyle K} N \phi_{f} c - 2 N \phi_{b} R c \\ & + 8 N r_{\scriptscriptstyle D} \phi_{b} c + 12 r_{\scriptscriptstyle K} N \psi_{f} c + 12 \mu_{f} N c + 3 N c^{2} {\phi_{b}^{2}} -c \phi_{b} {\Omega} - N R^{2} - R {\Omega} \\ & -8 N \psi_{b} r_{\scriptscriptstyle D} k c + 8 N \psi_{b} k r_{\scriptscriptstyle K} c - 8 N \phi_{b} r_{\scriptscriptstyle D} k c + 8 N \phi_{b} k r_{\scriptscriptstyle K} c \end{aligned} \right] }{(\phi_{f} + \upbeta) N c}, $$
(42)

where

$$ {\Omega} \equiv \sqrt{ \begin{aligned} & N (9 N c^{2} {\phi_{b}^{2}} + 2 N \phi_{b} R c + N R^{2} - 8 \upbeta N R c + 16 N r_{\scriptscriptstyle D} \psi_{b} c + 8 N t_{f} \gamma c \\ & - 8 \phi_{f} N R c + 8 r_{\scriptscriptstyle K} N \phi_{f} c + 16 N r_{\scriptscriptstyle D} \phi_{b} c+ 8 r_{\scriptscriptstyle K} N \psi_{f} c + 8 \mu_{f} N c + 4 t \gamma c \\ & -16 N \psi_{b} r_{\scriptscriptstyle D} k c + 16 N \psi_{b} k r_{\scriptscriptstyle K} c - 16 N \phi_{b} r_{\scriptscriptstyle D} k c + 16 N \phi_{b} k r_{\scriptscriptstyle K} c). \end{aligned} } $$

We further assume that

$$ \begin{aligned} & N (9 N c^{2} {\phi_{b}^{2}} + 2 N \phi_{b} R c + N R^{2} - 8 \upbeta N R c + 16 N r_{\scriptscriptstyle D} \psi_{b} c + 8 N t_{f} \gamma c \\ & - 8 \phi_{f} N R c + 8 r_{\scriptscriptstyle K} N \phi_{f} c + 16 N r_{\scriptscriptstyle D} \phi_{b} c+ 8 r_{\scriptscriptstyle K} N \psi_{f} c + 8 \mu_{f} N c + 4 t \gamma c \\ & -16 N \psi_{b} r_{\scriptscriptstyle D} k c + 16 N \psi_{b} k r_{\scriptscriptstyle K} c - 16 N \phi_{b} r_{\scriptscriptstyle D} k c + 16 N \phi_{b} k r_{\scriptscriptstyle K} c) >0 \end{aligned} $$

for the existence of an equilibrium as in Section 3.2.

Proof of Proposition 5

From Eq. (40), it is obvious through calculation that

$$ \frac{\partial \alpha^{**}}{\partial k} = \left\{ \frac{ 2 N (r_{\scriptscriptstyle K} - r_{\scriptscriptstyle D}) (\phi_{b} + \psi_{b})}{ {\Omega} } \right\} > 0. $$

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Tseng, PL., Guo, WC. Fintech, Credit Market Competition, and Bank Asset Quality. J Financ Serv Res 61, 285–318 (2022). https://doi.org/10.1007/s10693-021-00363-y

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  • DOI: https://doi.org/10.1007/s10693-021-00363-y

Keywords

  • Fintech
  • Banks
  • Credit market competition
  • Screening incentives
  • Capital regulation

JEL Classification

  • G18
  • G21
  • G23