Risk transfer versus cost reduction on two-sided microfinance platforms

Abstract

Microfinance can be an important tool for fighting global poverty by increasing access to loans and possibly lowering interest rates through microlending. However, the dominant mechanism used by online microfinance platforms, in which intermediaries administer loans, has profound implications for borrowers. Using an analytical model of microlending with intermediaries who disburse and service loans, we demonstrate that profit-maximizing intermediaries have an incentive to increase interest rates because much of the default risk is transferred to lenders. Borrower and lender interest rate elasticities can serve as disciplining mechanisms to mitigate this interest rate increase. Using data from Kiva.org, we find that interest rates do not affect lender decisions, which removes one of these disciplining mechanisms. Interest rates are high, around 38% on Kiva. In contrast, on an alternative microfinance platform that does not use intermediaries, Zidisha, interest rates are only around 10%, highlighting the dramatic impact of intermediaries on interest rates. We propose an alternative loan payback mechanism that still allows microfinance platforms to use intermediaries, while removing the incentive to increase interest rates due to the transfer of risk to lenders.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3

Notes

  1. 1.

    Crowdfunding is a specific type of crowdsourcing, a general term that implies a group of people is essential in accomplishing the end goal but does not require the contributions to be monetary in nature.

  2. 2.

    Source: “Crowdfunding Industry Report: Market Trends, Composition and Crowdfunding Platforms,” 2012, https://www.crowdsourcing.org.

  3. 3.

    Despite the high interest rates associated with microfinance, the average default rates (across FPs and time) are relatively low in our data (below 2%). However, the delinquency rates are fairly high at the level of about 11%. The distribution of default/delinquency rates, however, is extremely skewed. In some cases the default rates exceed 20% and the maximum is greater than 50%. The delinquency rates reach 100% for some FPs (see Table 1). One possible reason for the relatively low default rates is that other disciplining devices may keep interest rates (and thus default rates) in check, including group liability, dynamic incentives (if borrowers plan to borrow in the future), high default costs associated with reputation effects and/or public shaming, and mechanisms of repayment that often involve frequent, small payments and loan collection occurring in group meetings (Banerjee 2013). Additional disciplining mechanisms which may keep interest rates low include moral hazard on the borrower side if administration costs increase with interest rates (Banerjee and Duflo 2010), and FP reputation regarding social outcomes. Finally, because we are in a setting in which FPs have market power (unlike in many finance settings), the demand elasticity itself can serve as the disciplinary device; indeed, in the rare situations in which interest rates are low, such as the case of the Bolivian microfinance industry, the market is highly competitive - more competition increases demand elasticity, which increases the downward force on interest rates.

  4. 4.

    Zidisha is the only microfinance platform of which we are aware that connects borrowers directly to lenders without intermediaries. According to their website (https://www.zidisha.org/why-zidisha), “Zidisha’s direct person-to-person connection results in far lower cost for the entrepreneurs, and a more transparent and interesting experience for lenders. Our first-of-its-kind direct lending platform ensures that the profits go to the entrepreneurs (no cut of it goes to a bank or other intermediary).”

  5. 5.

    Hulme (2006) provide a nice history of social lending on the internet.

  6. 6.

    http://www.pbs.org/frontlineworld/stories/uganda601/video_index.html

  7. 7.

    Factors that alter the FPs’ expectation of loans being funded through Kiva, such as social and earned media exposures studied in Stephen and Galak (2012), will influence FPs’ decisions to provide loans.

  8. 8.

    The optimal levels can be obtained by maximizing the Lagrangian, \(\mathcal {L}=\log \alpha +\beta _{1}\log K_{0}+\beta _{2}\log L+\lambda (B-K_{0}p_{K}-Lp_{L})\).

  9. 9.

    We suppress the subscript for indexing FPs to avoid cluttering the notation.

  10. 10.

    Zidisha started its operations in October 2009.

  11. 11.

    The overlapping 10 countries and areas are Burkina Faso, Ghana, Guinea, Haiti, Indonesia, Kenya, Mexico, Niger, Senegal, and Zambia.

  12. 12.

    Note that this percentage of defaulted loans and the delinquency rate are different from the statistics presented in Table 2. The reason is simply that the statistics in these two Tables have different levels of aggregation that lead to rounding differences.

  13. 13.

    We note that the average APR across all loans is slightly different from the average APR across all FPs as reported in Table 2. This difference is due to differences in weighting when computing the average APRs.

  14. 14.

    We note that the high default rates of the Middle East may be due to its extensive political instability in the past decade.

  15. 15.

    We depict another figure only focusing on those Kiva loans issued when Zidisha operates (not reported), which shows similar insights.

  16. 16.

    If costs C(r) also increase with r, another disciplining mechanism would exist, but we have no cost data to test this relationship. However, this effect is documented in Banerjee and Duflo (2010).

  17. 17.

    Note that we also consider the same analyses using default rates instead of delinquency rates to measure loan risk and the insights remain the same.

  18. 18.

    One possible factor that may invalidate Zidisha’s entry as an instrument is if the platform chose countries with more low-risk borrowers to enter, hence the lower APR was the reason of Zidisha’s entry. We think this mechanism is unlikely because Zidisha had fairly high delinquency rates and consequently had to stop its operation for a brief time. Also, we control country and FP fixed effects. The within-FP-country variation related to Zidisha’s entry can further mitigate such a concern. Furthermore, in the appendix, we produce Table 6 to compare Kiva loan characteristics before and after the entries of Zidisha, showing that the loans have very similar characteristics. The similarity of loans implies the FPs tend to use the same screening criteria for borrowers before and after Zidisha, which leads to similar pools of loans.

  19. 19.

    We find the same using the regression discontinuity approach.

  20. 20.

    Another potential reason why a loan’s APR has inconsequential effect on the funding probability is that Kiva vaguely labeled the APR as the field partner’s “portfolio yield.” It might be difficult for lenders to perceive it as the interests and fees collected by the FP from borrowers. Recently, Kiva has changed the label to a more transparent “average cost to borrower.”

  21. 21.

    A full understanding of lender incentives is tangential to this paper’s goals, and there has been significant work in understanding these decisions in microfinance and crowdfunding applications (Galak et al. 2011; Agrawal et al. 2011; Stephen and Galak 2012; Kawai et al. 2014).

  22. 22.

    An alternative specification with the number of loans as the dependent variable gives similar results.

  23. 23.

    The rates are equivalent at the FP’s indifference point, which is intuitive since the only remaining force altering rates is due to the discrepancy in lending costs.

References

  1. Aaker, J., & Akutsu, S. (2009). Why do people give? The role of identity in giving. Stanford University Graduate School of Business Research Paper No. 2027.

  2. Agrawal, A.K., Catalini, C., Goldfarb, A. (2011). The geography of crowdfunding. NBER Working Paper No. 16820.

  3. Banerjee, A.V., & Duflo, E. (2010). Giving credit where it is due. Journal of Economic Perspectives, 24(3), 61–80.

    Article  Google Scholar 

  4. Banerjee, A.V. (2013). Microcredit under the microscope: What have we learned in the past two decades, and what do we need to know?. Annual Review of Economics, 5, 487–519.

    Article  Google Scholar 

  5. Banerjee, A., Chandrasekhar, A.G., Duflo, E., Jackson, M.O. (2013). The diffusion of microfinance. Science, 341, 363–371.

    Article  Google Scholar 

  6. Banerjee, A., Duflo, E., Glennerster, R., Kinnan, C. (2015). The miracle of microfinance? evidence from a randomized evaluation. American Economic Journal: Applied Economics, 7(1), 22–53.

    Google Scholar 

  7. Banerjee, A., Karlan, D., Zinman, J. (2015). Six randomized evaluations of microcredit: Introduction and further steps. American Economic Journal: Applied Economics, 7(1), 1–21.

    Google Scholar 

  8. Burtch, G., Ghose, A., Wattal, S. (2013). An empirical examination of the antecedents and consequences of contribution patterns in crowd-funded markets. Information Systems Research, 24(3), 499–519.

    Article  Google Scholar 

  9. Chu, M. (2007). Commercial returns at the base of the pyramid. Innovations: Technology, Governance, Globalization, 2(1-2), 115–146.

    Article  Google Scholar 

  10. Dieckmann, R. (2007). Microfinance: An emerging investment opportunity. Technical report, Deutsche Bank Research.

  11. Duarte, J., Siegel, S., Young, L. (2012). Trust and credit: The role of appearance in peer-to-peer lending. The Review of Financial Studies, 25(8), 2455–2484.

    Article  Google Scholar 

  12. Flippen, A.R., Hornstein, H.A., Siegal, W.E., Weitzman, E.A. (1996). A comparison of similarity and interdependence as triggers for in-group formation. Personality and Social Psychology Bulletin, 22(9), 882–893.

    Article  Google Scholar 

  13. Galak, J., Small, D., Stephen, A.T. (2011). Microfinance decision making: A field study of prosocial lending. Journal of Marketing Research, 48(SPL), S130–S137. https://doi.org/10.1509/jmkr.48.SPL.S130.

    Article  Google Scholar 

  14. Hulme, M.K.C. (2006). Wright Internet based social lending: Past present and future. Technical report, Social Futures Observatory.

  15. Iyer, R., Khwaja, A.I., Luttmer, E.F., Shue, K. (2015). Screening peers softly: Inferring the quality of small borrowers. Management Science, 62(6), 1554–1577. https://doi.org/10.1287/mnsc.2015.2181.

    Article  Google Scholar 

  16. Kawai, K., Onishi, K, Uetake, K. (2014). Signaling in online credit markets. working paper.

  17. Kent, D., & Dacin, M.T. (2013). Bankers at the gate: Microfinance and the high cost of borrowed logics. Journal of Business Venturing, 28, 6.

    Article  Google Scholar 

  18. Kogut, T., & Ritov, I. (2005a). The “identified victim” effect: an identified group, or just a single individual?. Journal of Behavioral Decision Making, 18(3), 157–167.

  19. Kogut, T., & Ritov, I. (2005b). The singularity effect of identified victims in separate and joint evaluations. Organizational Behavior and Human Decision Processes, 97(2), 106–116.

  20. Kogut, T., & Ritov, I. (2007). “One of us”: Outstanding willingness to help save a single identified compatriot. Organizational Behavior and Human Decision Processes, 104(2), 150–157.

    Article  Google Scholar 

  21. Krebs, D. (1975). Empathy and altruism. Journal of Personality and Social Psychology, 32(6), 1134–1146.

    Article  Google Scholar 

  22. Lin, M., Prabhala, N.R., Viswanathan, S. (2013). Judging borrowers by the company they keep: Friendship networks and information asymmetry in online peer-to-peer lending. Management Science, 59(1), 17–35. https://doi.org/10.1287/mnsc.1120.1560.

    Article  Google Scholar 

  23. Liu, W., & Aaker, J. (2008). The happiness of giving:the time-ask effect. Journal of Consumer Research, 35(3), 543–557.

    Article  Google Scholar 

  24. Michels, J. (2012). Do unverifiable disclosures matter? evidence from peer-to-peer lending. Accounting Review, 87(4), 1385–1413.

    Article  Google Scholar 

  25. Nevo, A. (2001). Measuring market power in the ready-to-eat cereal industry. Econometrica, 69(2), 307–342. http://www.jstor.org/stable/2692234.

    Article  Google Scholar 

  26. Phillips, R. (2013). Optimizing prices for consumer credit. Journal of Revenue and Pricing Management, 12(4), 360–377.

    Article  Google Scholar 

  27. Pope, D.G., & Sydnor, J.R. (2011). What’s in a picture? evidence of discrimination from prosper.com. Journal Human Resources, 46(1), 53–92.

    Google Scholar 

  28. Ravina, E. (2012). Love & loans: The effect of beauty and personal characteristics in credit markets. working paper.

  29. Rossi, P.E. (2014). Invited paper – even the rich can make themselves poor: A critical examination of iv methods in marketing applications. Marketing Science, 33 (5), 655–672. https://doi.org/10.1287/mksc.2014.0860.

    Article  Google Scholar 

  30. Small, D.A., & Simonsohn, U. (2008). Friends of victims: Personal experience and prosocial behavior. Journal of Consumer Research, 35(3), 532–542.

    Article  Google Scholar 

  31. Small, D.A., & Verrochi, N.M. (2009). The face of need: Facial emotion expression on charity advertisements. Journal of Marketing Research, 46(6), 777–787.

    Article  Google Scholar 

  32. Stephen, A., & Galak, J. (2012). The effects of traditional and social earned media on sales: A study of a microlending marketplace. Journal of Marketing Research, 49(5), 624–639. http://www.journals.marketingpower.com/doi/abs/10.1509/jmr.09.0401.

    Article  Google Scholar 

  33. Stotland, E., & Dunn, R.E. (1963). Empathy, self-esteem, and birth order. The Journal of Abnormal and Social Psychology, 66(6), 532–540.

    Article  Google Scholar 

  34. Wei, Y., Yildirim, P., den Bulte, C.V., Dellarocas, C. (2016). Credit scoring with social network data. Marketing Science, 35(2), 234–258.

    Article  Google Scholar 

  35. Weining, B., Ni, J., Singh, S. (2017). Informal lending in emerging markets. forthcoming at Marketing Science.

  36. Zephyr, A.M. (2004). Money is not enough: Social capital and microcredit. Issues in Political Economy, 13, 1–12.

    Google Scholar 

  37. Zhang, J., & Lui, P. (2012). Rational herding in microloan markets. Management Science, 58(5), 892–912. https://doi.org/10.1287/mnsc.1110.1459.

    Article  Google Scholar 

Download references

Acknowledgments

We would like to thank Manuel Adelino, Wilfred Amaldoss, Preyas Desai, Pedro Gardete, Debu Purohit, and participants at the 2015 INFORMS Marketing Science Conference for valuable comments. We would also like to acknowledge the excellent feedback we received from the editor and two anonymous reviewers. We also thank Huanxin Wu, Nazli Gurdamar and Boya Xu for excellent research assistance. All errors are our own.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Bryan Bollinger.

Appendices

Appendix A: Proof of Claim 1

Proof

The probability of borrowing Kiva loan up to the amount of K is given by

$$ y(r)= 1-{\Phi}_{\epsilon}\left( \beta_{1}\log\left( \frac{\overline{K}_{0}}{\overline{K}_{0}+K}\right)+\beta_{2}\log\left( \frac{L^{*}+(K_{0}^{*}-\overline{K}_{0})\frac{p_{K}}{p_{L}}}{L^{*}+(K_{0}^{*}-\overline{K}_{0})\frac{p_{K}}{p_{L}}-K\frac{p(r)}{p_{L}}}\right)\right). $$
(11)

Taking the derivative of y(r) with respect to \(\overline {K}_{0}\), we have

$$\begin{array}{@{}rcl@{}} \frac{\partial y(r)}{\partial\overline{K}_{0}} \!& = & \left( \frac{-\phi_{\epsilon}\left( \beta_{1}\log\left( \frac{\overline{K}_{0}}{\overline{K}_{0}+K}\right)+\beta_{2}\log\left( \frac{L^{*}+(K_{0}^{*}-\overline{K}_{0})\frac{p_{K}}{p_{L}}}{L^{*}+(K_{0}^{*}-\overline{K}_{0})\frac{p_{K}}{p_{L}}-K\frac{p(r)}{p_{L}}}\right)\right)}{1-{\Phi}_{\epsilon}\left( \beta_{1}\log\left( \frac{\overline{K}_{0}}{\overline{K}_{0}+K}\right)+\beta_{2}\log\left( \frac{L^{*}+(K_{0}^{*}-\overline{K}_{0})\frac{p_{K}}{p_{L}}}{L^{*}+(K_{0}^{*}-\overline{K}_{0})\frac{p_{K}}{p_{L}}-K\frac{p(r)}{p_{L}}}\right)\right)}\right)\cdot\\ & & \left( \!\beta_{1}\frac{K}{\overline{K}_{0}(\overline{K}_{0}\,+\,K)}\,+\,\beta_{2}\frac{K\frac{p_{K}}{p_{L}}\frac{p(r)}{p_{L}}}{\left[L^{*}\,+\,(K_{0}^{*}\,-\,\overline{K}_{0})\frac{p_{K}}{p_{L}}\right]\left[L^{*}\,+\,(K_{0}^{*}\,-\,\overline{K}_{0})\frac{p_{K}}{p_{L}}\,-\,K\frac{p(r)}{p_{L}}\right]}\right). \end{array} $$

The first term (\(\frac {-\phi _{\epsilon }(.)}{1-{\Phi }_{\epsilon }(.)}\)) is negative, and the second and third terms in the brackets are non-negative. Hence, the derivative is negative. □

Appendix B: Proofs of Proposition and Corollary

Proof of Proposition 1.

Total expected profits were given in Eq. 8 as:

$$ \pi(r)=y(r)\left[F(r)p(r)-\widetilde{K}+\left( \widetilde{K}-F(r)\frac{K}{T}-C\right)l(r)\right], $$
(12)

in which profits for a commercially financed loan are:

$$\begin{array}{@{}rcl@{}} \pi^{C}(r) & = & F(r)p(r)-\widetilde{K}, \end{array} $$
(13)

and expected profits for a loan offered through microfinance are:

$$\begin{array}{@{}rcl@{}} \pi^{M}(r) & = & \pi^{C}(r)+\left( \widetilde{K}-F(r)\frac{K}{T}-C\right)l(r). \end{array} $$
(14)

For readability, we omit the function arguments in the proof. Taking the derivative of total expected profits yields:

$$\begin{array}{@{}rcl@{}} \frac{\partial\pi}{\partial r} & = & \eta_{y}\frac{y(r)}{r}\pi^{M}+y(r)[F^{\prime}(r)p(r)+F(r)\frac{\partial p(r)}{\partial r}+\widetilde{K}\frac{\partial l(r)}{\partial r}-F(r)\frac{K}{T}\frac{\partial l(r)}{\partial r}\\ &&-C\frac{\partial l(r)}{\partial r}-F^{\prime}(r)\frac{K}{T}l(r)]\\ & = & \frac{y(r)}{r}\left[\eta_{y}\left( \left( F(r)p(r)-\widetilde{K}\right)+\left( \widetilde{K}-F(r)\left( \frac{K}{T}\right)-C\right)l(r)\right)\right.\\ & & \left.+\left( rF^{\prime}(r)p(r)+rF(r)\frac{\partial p(r)}{\partial r}+\left( \widetilde{K}-F(r)\left( \frac{K}{T}\right)-C\right)\eta_{l}l(r)\right.\right.\\ &&\left.\left.-rF^{\prime}(r)\frac{K}{T}l(r)\right)\right]. \end{array} $$

Setting this partial derivative to zero, we can define:

$$\begin{array}{@{}rcl@{}} {\Theta}_{1}(r) & \equiv & p(r)+ \end{array} $$
(15)
$$\begin{array}{@{}rcl@{}} & & \frac{1}{\eta_{y}F(r)+rF^{\prime}(r)}\left[-\eta_{y}\widetilde{K}+rF(r)\frac{\partial p(r)}{\partial r} \right. \end{array} $$
$$\begin{array}{@{}rcl@{}} &&+ \left. l(r)\left( \eta_{y}\left( \widetilde{K}-F(r)\left( \frac{K}{T}\right)-C\right)+\eta_{l}\left( \widetilde{K}-F(r)\left( \frac{K}{T}\right)-C\right) \right.\right. \end{array} $$
$$\begin{array}{@{}rcl@{}} &&\left.\left.-rF^{\prime}(r)\frac{K}{T}\right)\right], \end{array} $$

such that Θ1(rM) = 0 at the optimal interest rate rM.

Without microfinance, we can set l(r) and ηl to 0. This yields:

$$\begin{array}{@{}rcl@{}} {\Theta}_{2}(r) & \equiv & p(r)+\frac{1}{\eta_{y}F(r)+rF^{\prime}(r)}\left[-\eta_{y}\widetilde{K}+rF(r)\frac{\partial p(r)}{\partial r}\right], \end{array} $$
(16)

which is equal to zero at the optimal interest rate rC without microfinance.

We can calculate the difference in these two functions as:

$$\begin{array}{@{}rcl@{}} {\Theta}_{2}-{\Theta}_{1} & = & -\frac{l(r)}{\eta_{y}F(r)+rF^{\prime}(r)}\left[\eta_{y}\left( \widetilde{K}-F(r)\left( \frac{K}{T}\right)-C\right)\right.\\ &&\left.+\eta_{l}\left( \widetilde{K}-F(r)\left( \frac{K}{T}\right)-C\right)-rF'(r)\frac{K}{T}\right]. \end{array} $$

Here, we make one final assumption:

Assumption 5

Define Θ ≡Θ2 −Θ1 . Θ is increasing and satisfies the single-crossing condition if ∃r|Θ(r) = 0.

This assumption is benign because the expression is negative at r = 0. We know the first term, \(-\frac {l(r)}{\eta F+rF^{\prime }}\), is negative, because from Assumption 3, we have that F(r) ≤ 0, ηy is negative from Assumption 1, ηl is negative from Assumption 2, and F(r) is positive. Next, we know \(\widetilde {K}-F\left (\frac {K}{T}\right )-C\) is positive, otherwise the FP would not post the loan and so the first and second terms in the square brackets are negative. The third term is the only non-negative term, because F(r) is negative. At the optimal interest rate without microfinance, rC, we have that Θ2(rC) = 0. Therefore Θ2 (rC) −Θ1 (rC) < 0, at the optimal interest rate without microfinance if and only if the third (risk-transfer) term is smaller in magnitude than the combined first two terms. By the single crossing property, this means that for all r < rC2 (rC) −Θ1 (rC) < 0, and so for the optimal rate with microfinance, rM, we have that rM < rC. Conversely, if the third term is larger in magnitude than the other two terms, we have that Θ2 (rC) −Θ1 (rC) > 0,and therefore rM > rC.

Proof of Corollary 1.

From Eq. 9, and by the implicit function theorem, we have that:

$$\frac{dr_{M}}{dz}=-\frac{\frac{\partial}{\partial z}\frac{\partial\pi(r_{M})}{\partial r}}{\frac{\partial}{\partial r}\frac{\partial\pi(r_{M})}{\partial r}}=-\frac{\frac{\partial\eta_{y}}{\partial z}\pi^{M}}{r\frac{\partial^{2}\pi^{M}}{\partial r^{2}}+\frac{\partial\eta_{y}}{\partial r}\pi^{M}}>0 $$

The numerator is positive by definition, and the first term in the denominator is negative by Assumption 4. The second term in the denominator is negative above the inflection point in the choice probability expression since \(\frac {\partial -\phi (r)}{\partial r}>0\) for y > .5 (see Eq. 3). Thus the entire expression is positive and the optimal interest rate increases with less elastic demand. □

Appendix C: Alternative Mechanism

Profits for a microfinance-funded loan under our alternative payment mechanism A are

$$\begin{array}{@{}rcl@{}} \pi^{Funded|A}(r) & = & F(r)\left( p(r)\right)-N\frac{K}{T}-C, \end{array} $$
(17)

where the FP receives monthly payments p(r) from the borrower but pays back the lenders with the monthly contribution to principal, L/T, regardless of whether the borrower defaults. N is the total discounted number of payments (equal to T if there is no discounting by FPs). Note that TNF. The total expected profits for a loan posted under this alternative are:

$$\begin{array}{@{}rcl@{}} \pi^{A}(r) & = & \left( F(r)p(r)-\widetilde{K}\right)\left( 1-l(r)\right)+\left( F(r)\left( p(r)\right)-N\frac{K}{T}-C\right)l(r) \\ & = & \left( F(r)p(r)-\widetilde{K}\right)+\left( \widetilde{K}-N\frac{K}{T}-C\right)l(r) \\ & = & \pi^{C}(r)+\left( \widetilde{K}-N\frac{K}{T}-C\right)l(r). \end{array} $$
(18)

The expected profit for a loan the FP offers to a borrower is:

$$ \pi(r)=y(r)\,\pi^{A}(r). $$
(19)

Taking the derivative of profits with respect to r, we have:

$$\begin{array}{@{}rcl@{}} \frac{\partial\pi(r)}{\partial r} & = & \eta_{y}\frac{y(r)}{r}\pi^{A}+y(r)\left[F^{\prime}(r)p(r)+F(r)\frac{\partial p(r)}{\partial r}+\widetilde{K}\frac{\partial l(r)}{\partial r}\right.\\ &&\left.-N\frac{K}{T}\frac{\partial l(r)}{\partial r}-C\frac{\partial l(r)}{\partial r}\right]\\ & = & \frac{y(r)}{r}\left[\eta_{y}\left( \left( F(r)p(r)-\widetilde{K}\right)+\left( \widetilde{K}-N\left( \frac{K}{T}\right)-C\right)l(r)\right)\right.\\ & & \left.+\left( rF^{\prime}(r)p(r)+rF(r)\frac{\partial p(r)}{\partial r}+\left( \widetilde{K}-N\left( \frac{K}{T}\right)-C\right)\eta_{l}l(r)\right)\right]. \end{array} $$

Similar to before, we can define:

$$\begin{array}{@{}rcl@{}} {\Theta}_{3}(r) & \equiv & p(r)+ \end{array} $$
(20)
$$\begin{array}{@{}rcl@{}} & & \frac{1}{\eta_{y}F(r)+rF^{\prime}(r)}\left[-\eta_{y}\widetilde{K}+rF(r)\frac{\partial p(r)}{\partial r}+ \right. \end{array} $$
$$\begin{array}{@{}rcl@{}} & & \left. l(r)\left( \eta_{y}\left( \widetilde{K}-N\left( \frac{K}{T}\right)-C\right)+\eta_{l}\left( \widetilde{K}-N\left( \frac{K}{T}\right)-C\right)\right)\right]. \end{array} $$
(21)

Assumption 6

Θ ≡Θ3 −Θ2 is increasing and satisfies the single-crossing condition.

This assumption yields a unique solution rA to Eq. 21 over the support of the parameters. This assumption allows us to compare the situations with and without microfinance with the alternative mechanism.

We can again calculate the differences in the Θ functions:

$$\begin{array}{@{}rcl@{}} {\Theta}_{3}-{\Theta}_{2} & = & \frac{l(r)}{\eta_{y}F(r)\,+\,rF^{\prime}(r)}\left[\!\eta_{y}\left( \!\widetilde{K}\,-\,N\left( \frac{K}{T}\right)\,-\,C\right)\!+\eta_{l}\left( \widetilde{K}-N\left( \frac{K}{T}\right)\!-C\right)\right]. \end{array} $$

These terms are the same as with the current microfinance payment mechanism with the exception that N appears on the right-hand side inside the braces instead of F, and the term that includes F, which was the risk-transfer term, is absent. Because both terms inside the brackets are negative in value, the interest rate must be lower due to Kiva, from the single-crossing assumption. The intuition is that by having the FPs pay back lenders irrespective of default, the upward force on rates from risk transfer has been removed.

Appendix D: Simulations

Current Mechanism

We use numerical simulations to demonstrate the dependence of the interest rate on the demand and demand elasticity with and without the presence of microfinance, in order to demonstrate microfinance’s effect on the optimal interest rate. For these simulations, we set the loan duration to be one year and loan amount of 0.61, which is the average loan size relative to the country’s GDP per capita in our data. For the first set of simulations, we assume that additional loan disbursement costs through microfinance are low, 10% of the loan amount, and that they do not increase with interest rates (if costs increased with interest rates, this would further push rates down). We assume that the cost of borrowing for the FP is 10% of the value of the loan (which we later vary). We set demand to be 0.5 for a range of demand elasticities between -0.5 and -1.0. The qualitative relationships are robust to changes in the parameter values, which are used for illustrative purposes.

We assume the probability of making each payment is a time-invariant function of r, δ(r), so that delinquent payments (which occur with probability 1 − δ(r)) are not made; the borrower continues to make future payments with probability δ(r):

$$\begin{array}{@{}rcl@{}} F(r)\!\equiv\!\sum\limits_{m = 1}^{T}\left( \rho\delta(r)\right)^{m} & \,=\,\frac{1-\left( \rho\delta(r)\right){}^{T + 1}}{1-\rho\delta(r)}\,-\,1\,=\,\frac{-\left( \rho\delta(r)\right){}^{T + 1}+\rho\delta(r)}{1-\rho\delta(r)} & \,=\,\frac{\rho\delta(r)\left( 1\,-\,\left( \rho\delta(r)\right){}^{T}\right)}{1\,-\,\rho\delta(r)}.\\ \end{array} $$
(22)

These assumption are not needed, but they help with the interpretation of the simulations. Because δ(r) can be easily interpreted (as “1−monthly delinquency probability”), we will vary δ(r) in the simulations in order to vary F(r).

The FPs’ discount rate and the monthly delinquency probability have the same effect because a higher value of either will lower the net present value of the loan. For the simulations, we set the FPs’ discount rate to be ρ = 0.99 and alter the delinquency rate function. We specify this function as:

$$ \delta(r)= 1-\kappa_{1}\exp((r-.5)\kappa_{2}). $$
(23)

This allows us to modify the level of delinquency rate as well as the curvature of the delinquency rate function by changing κ1 and κ2. To show the effect of the two κ parameters on the shape of the delinquency rate function, we plot the delinquency rate function for different values of the κ parameters in Fig. 4. The first figure shows the function for a lower initial delinquency rate at r = 0 with κ1 = 0.01 for κ2 = 5 and 10, and the second for a higher initial delinquency rate with κ1 = 0.02 for the same values of κ2. A larger κ2 results in a greater curvature of the delinquency function (shown in Fig. 4 with the dashed line).

Fig. 4
figure4

Delinquency Rate Parameterization

Next, we compare the optimal APRs as a function of both demand and demand elasticity. The first derivative of the delinquency rate function (23) with respect to interest rates is − κ1κ2 exp((r − .5)κ2), which measures the impact of interest rates on the level of delinquency risk. In Fig. 5, we show the optimal interest rates with and without microfinance as the magnitude of the first derivative becomes larger, which is achieved by increasing the value of κ1 or κ2. In Fig. 5, the delinquency rate is set at κ1 = 0.01 in the left two graphs, with the bottom graph having the larger κ2, i.e., delinquency increases more rapidly with interest rate. With a larger effect of rate on delinquency, there is a larger risk transfer effect. Hence the graphs of the optimal APRs with and without microfinance cross at a lower rate. In the right two figures, we use the same value for κ2, but double κ1 - the effect is to increase the disparity between the rates with and without microfinance - the rate at which the two curves cross is the same as with the lower κ1 . Thus the greater the magnitude of the first derivative of delinquency with respect to interest rate, the greater the differences in the optimal interest rates with and without microfinance. The second derivative of delinquency with respect to interest rate determines the point at which demand is inelastic enough such that interest rates become higher with microfinance.

Fig. 5
figure5

Comparison of APRs between Microfinance Loans and Non-Microfinance Loans, High Default Rate

Proposed Alternative Mechanism

In this subsection, we again use simulations to calculate optimal interest rates, but under our proposed payback mechanism. In Fig. 6, we demonstrate how the optimal interest rate varies as a function of demand elasticity under our proposed alternative mechanism. In contrast to the current mechanism, as demand becomes more inelastic, the optimal APR under the proposed mechanism approaches the level without microfinance, but never exceeds it. The discrepancy in interest rates is driven by the reduction of lending costs, while the risk transfer effect is completely removed. As stated by Proposition 2, the optimal interest rate is always below that without microfinance.

Fig. 6
figure6

Comparison of APRs between Microfinance Loans and Non-Microfinance Loans, Alternative Mechanism

In Fig. 7, we compare the FP profits and optimal interest rates as a function of the additional costs of administering a loan through microfinance, at the observed demand elasticity in the data. We plot these variables both when using and when not using microfinance, and we use a thick, gray line to designate the profits and optimal interest rate for the option that maximizes profits. As the administrative costs increase, the profits when using microfinance go down for the FPs and the optimal interest rates go up. Essentially, any additional administrative cost of working with the microfinance platform reduces the downward pressure on rates that results from the lower costs of dispersing loans (due to the refinancing), and so the upward force due to risk transfer dominates. If costs become too high, the FP choses not to post the loan because its profits become higher when not using the microfinance site (at which point the optimal APR drops back down to what it would be without microfinance). From a consumer welfare perspective, it is the intermediate level of costs which cause concern under the current mechanism, since the FPs still choose to use the microfinance platform but the interest rates are higher when doing so. It is thus essential that microfinance sites keep administrative costs to a minimum for the FPs, otherwise rates may become higher than in the absence of microfinance.

Fig. 7
figure7

Comparison of FP Profit and APRs between Microfinance Loans and Non-Microfinance Loans as Administrative Costs Increase

At the observed demand elasticity in the data, and using our parameterization of the demand curve, the interest rate with microfinance exceeds that without microfinance (under the current mechanism) as soon as extra costs of administering microfinance loans exceeds 1.5% of the loan amount. In sharp contrast, under the alternative repayment mechanism, if costs with microfinance become high enough, the FP may decide not to use microfinance, but in all cases the optimal interest rate remains below the rate without microfinance.Footnote 23 In cases with minimal additional costs, rates would be considerably lower with microfinance than without microfinance, under our proposed mechanism.

Appendix E: Comparison of Kiva Loans before and after Zidisha

Table 6 Summary Statistics of Kiva Loan Characteristics before and after Zidisha

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bollinger, B., Yao, S. Risk transfer versus cost reduction on two-sided microfinance platforms. Quant Mark Econ 16, 251–287 (2018). https://doi.org/10.1007/s11129-018-9198-0

Download citation

Keywords

  • Microfinance
  • Crowdfunding
  • Two-sided platforms
  • FinTech
  • Lending
  • Pricing
  • Risk transfer

JEL Classification

  • D21
  • D22
  • D47
  • D53
  • L11
  • L2
  • L3