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Determinants of Market Power in the Peruvian Regulated Microfinance Sector


The objective of this study is to analyze the evolution and determinants of market power in Peru’s regulated microfinance sector during the period of January 2003 to June 2016. We estimate both a conventional Lerner index (LICON) and an efficiency-adjusted Lerner index (LIADJ) using information from a wide panel of microfinance institutions (MFIs), thus finding that the LIADJ is significantly greater than the LICON. This result confirms that not considering MFIs’ inefficiency leads to an underestimation of their market power. Both indices decreased until 2014, which indicates that regulated MFIs’ market power decreased significantly for more than a decade. Beginning in 2015, market power significantly grew; the largest entities as well as those with the highest efficiency have greater market power. This last result evidences the fulfillment of the efficient structure (ES) hypothesis. In addition, a less elastic demand for microcredit, a lower default risk, as well as the processes of mergers, takeovers, and changes in the business structure of some MFIs, increase market power. Finally, the MFIs that operate in localized areas exhibit greater market power.

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  1. 1.

    Market power is a broader concept than is the financial margin because it incorporates total rather than solely financial costs into the marginal cost. In fact, as an indicator of competition, market power is a determinant of the financial margin (Cuéllar-Fernández et al. 2016).

  2. 2.

    There is also an unregulated and unsupervised microfinance sector comprises cooperatives and nongovernmental organizations with microcredit programs. There exists no official record of these entities’ total loans and clients. The most important of these institutions voluntarily report information to the MIX Market database. According to this information, in 2015, 7% of the total microcredits provided by the Peruvian microfinance sector were offered by these unregulated and unsupervised entities. Given their reduced participation in the microcredit supply and the lack of official information about these entities, they are not considered in this analysis.

  3. 3.

    See Appendix for the model’s algebraic formulation.

  4. 4.

    This assumption may be relaxed to permit market power’s existence in the deposit market. The result would be similar to that obtained for the credit market, due to which market power’s evolution and determinants in the deposit market may be analyzed separately from the credit market. However, a lack of statistical information that distinguishes the costs associated with both products hinders the construction of separate costs for loans and deposits, thus not allowing a market power analysis for both the credit and deposit markets.

  5. 5.

    Under this assumption, each MFI’s demand depends on a fraction of the total demand it serves, the average market interest rate, and the total demand elasticity for microcredits.

  6. 6.

    According to the theoretical model developed in the Appendix, the number of MFIs does not clearly affect the Lerner index, whose partial derivate with respect to the total number of entities depends on the difference between demand elasticity for loans from MFI “k” and the total demand elasticity for microloans.

  7. 7.

    See SBS (2003).

  8. 8.

    Resolution SBS 1276–2002, which approved the regulations for the entry of MFIs into the Lima market.

  9. 9.

    Legislative Decree 1028/2008, which amends Article 290 of Law 28677, General Law on the Financial System and the Insurance System and Organic Law on the Superintendency of Banking, Insurance, and Private Pension Funds Administrators.

  10. 10.

    The HHI equals the sum of the squares of all MFIs’ market shares in the microcredit market. The HHI formula is\( {\mathrm{HHI}}_t=\sum \limits_{i=1}^n{\mathrm{MS}}_{it}^2 \), where MSit represents the market share (expressed as a percentage) of MFI i at time t. Market share is calculated from the MFI’s participation in the microcredit market’s total loans.

  11. 11.

    We add the default risk’s cost to total costs because, when lending to high-risk clients, MFIs incur high costs of managing this risk by establishing provisions for expected losses. Provisions do not constitute effective outflows of the entity’s resources, but they reduce—in accounting terms—the available capital constituting an important cost for the institution.

  12. 12.

    We employ the xtscc command in Stata to perform the fixed effects model with Driscoll and Kraay standard errors. This method provides robust standard errors to very general forms of cross-sectional and temporal dependence; see Hoechle (2007) for further details about this command.

  13. 13.

    For a detailed presentation on stochastic frontiers, see Kumbhakar and Lovell (2003) and Kumbhakar et al. (2015).

  14. 14.

    To estimate these frontiers, we employ the sfpanel command in Stata (see Belotti et al. 2013).

  15. 15.

    Nonprimary GDP includes the nonprimary manufacturing, electricity and water, construction, trade, and service industries and is therefore a more appropriate measure of internal economic activity.

  16. 16.

    See Greene (2012).

  17. 17.

    The reported results may not be changed via a larger or smaller lag; see Appendix, Table 7 for the test results. For further details regarding the endogeneity test, see Baum et al. (2007).

  18. 18.

    At the outset, we had data for 42 MFIs: 13 CMACs, 2 banks specializing in microfinance, 13 CRACs, and 14 EDPYMEs. Some entities changed their business structure, were taken over by other entities, or were merged with one another. We excluded from the panel those that were taken over at an early stage because they provided few observations. Thus, the number of MFIs in the final database was 36. On the other hand, of the 8 mergers, takeovers, and business structure changes that occurred during the period analyzed, 5 were considered in the analysis because they represented large changes in the MFIs’ volume of total loan portfolio and equity.

  19. 19.

    The results of all Im–Pesaran–Shin tests are available upon request.

  20. 20.

    See Appendix for the estimates of the translog cost function as well as the cost and alternative profit frontiers (Table 4, 5 and 6).

  21. 21.

    Quasi-fixed inputs are only adjustable in the long run, and it can be very difficult for entities to respond to short-run price fluctuations (Kumbhakar et al. 2015). Thus, in a realistically dynamic economy, firms cannot always be on the frontier.

  22. 22.

    This result is in line with the findings of Koetter et al. (2012) and Ariss (2010) in the banking literature.

  23. 23.

    Available upon request.

  24. 24.

    We employed the xtivreg2 command in Stata to estimate the fixed effect IV models; see Schaffer (2005) for further details regarding this command.

  25. 25.

    We employed the xtserial command in Stata to perform the Wooldridge test for serial autocorrelation; see Drukker (2003) for further details regarding this command.

  26. 26.

    See Baum et al. (2007) for details on the fixed effect IV model’s diagnostic tests.

  27. 27.

    See Appendix, Table 7 for results.


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We assume that MFIs behave as price fixers in the loan market and that they are subject to a given deposit rate in their liabilities. Moreover, the model takes into account product differentiation by assuming that each MFI offers a type of loan “k” differentiated from that of its competitors, the demand function of which is as follows:

$$ {L}_k=\frac{L_0}{N}-\frac{b}{N-1}\sum \limits_{j\ne k}^N\left({r}_k-{r}_j\right)-\frac{r_LB}{N} $$

Lk is the demand for loans from MFI “k,” L0 is the aggregate demand for loans, N is the number of MFIs, b is the elasticity of demand for loans from MFI “k,” rk is the loan interest rate of MFI krj is the loan interest rate of MFI “j,” rL is the average loan interest rate \( {r}_{\mathrm{L}}=\frac{\sum \limits_{k=1}^N{r}_k}{N} \), and B is the total demand elasticity for loans in the microfinance system with respect to the average loan interest rate.

The MFIs maximize their expected profits by selecting an interest rate rk. The expected risk-adjusted income is (1 − βk)rkLk, where βk is the risk of insolvency. On the other hand, the costs are given by rDDk + Ck(Lk, Dk), where rD is the deposit rate, which is assumed to be equal for all MFIs and Dk and Ck(Lk, Dk) represent the deposits and operating costs of MFI k, respectively.

Given that Dk = Lk + Rk, where Rk are the minimum reserves required and these are proportional to the volume of deposits collected and Rk = αDk, where α is the coefficient of required reserves, therefore:

$$ {\displaystyle \begin{array}{l}{D}_k={L}_k+{R}_k\\ {}{D}_k={L}_k+\alpha {D}_k\\ {}{L}_k=\left(1-\alpha \right){D}_k\\ {}{D}_k=\frac{L_k}{\left(1-\alpha \right)}\end{array}} $$

Each MFI maximizes the following objective function:

$$ \underset{r_k}{\operatorname{Max}}{\pi}_k=\left(1-{\beta}_k\right){r}_k{L}_k-{r}_D{D}_k-{C}_k\left({L}_k,{D}_k\right) $$

By taking Eq. 9 into account and replacing it in Eq. 10:

$$ \underset{r_k}{\operatorname{Max}}{\pi}_k=\left(1-{\beta}_k\right){r}_k{L}_k-{r}_D\frac{L_k}{\left(1-\alpha \right)}-{C}_k\left({L}_k\right) $$

The first-order condition is as follows:

$$ {\displaystyle \begin{array}{l}\frac{\partial {\pi}_k}{\partial {r}_k}=\left(1-{\beta}_k\right){L}_k+\left(1-{\beta}_k\right){r}_k\frac{\partial {L}_k}{\partial {r}_k}-\frac{r_D}{\left(1-\alpha \right)}\frac{\partial {L}_k}{\partial {r}_k}-\frac{\partial {C}_k\left({L}_k\right)}{\partial {L}_k}\frac{\partial {L}_k}{\partial {r}_k}=0\\ {}\left[\left(1-{\beta}_k\right){r}_k-\frac{r_D}{\left(1-\alpha \right)}-\frac{\partial {C}_k\left({L}_k\right)}{\partial {L}_k}\right]\frac{\partial {L}_k}{\partial {r}_k}=-\left(1-{\beta}_k\right){L}_k\end{array}} $$

Given from Eq. 8 that:

$$ \frac{\partial {L}_k}{\partial {r}_k}=-\frac{(b)N-1}{N-1}-\frac{B}{N^2}=-\left(b+\frac{B}{N^2}\right) $$

By replacing Eq. 13 in Eq. 12:

$$ {\displaystyle \begin{array}{l}\left[\left(1-{\beta}_k\right){r}_k-\frac{r_D}{\left(1-\alpha \right)}-\frac{\partial {C}_k\left({L}_k\right)}{\partial {L}_k}\right]\left(-1\right)\left(b+\frac{B}{N^2}\right)=-\left(1-{\beta}_k\right){L}_k\\ {}\left[\left(1-{\beta}_k\right){r}_k-\frac{r_D}{\left(1-\alpha \right)}-\frac{\partial {C}_k\left({L}_k\right)}{\partial {L}_k}\right]\left(b+\frac{B}{N^2}\right)=\left(1-{\beta}_k\right){L}_k\\ {}\left(1-{\beta}_k\right){r}_k-\frac{r_D}{\left(1-\alpha \right)}-\frac{\partial {C}_k\left({L}_k\right)}{\partial {L}_k}=\left(1-{\beta}_k\right){L}_k\frac{1}{\left(b+\frac{B}{N^2}\right)}\end{array}} $$

If the MFIs are subject to similar demand curves, the loan interest rate will be the same for all entities. So, rk = rj and Eq. 8 will now be as follows:

$$ {L}_k=\frac{L_0}{N}-\frac{r_kB}{N} $$

By replacing Eq. 15 in Eq. 14:

$$ \left(1-{\beta}_k\right){r}_k-\frac{r_D}{\left(1-\alpha \right)}-\frac{\partial {C}_k\left({L}_k\right)}{\partial {L}_k}=\left(1-{\beta}_k\right)\left(\frac{L_0}{N}-\frac{r_kB}{N}\right)\frac{1}{\left(b+\frac{B}{N^2}\right)} $$

By dividing both sides by rk:

$$ \frac{\left(1-{\beta}_k\right){r}_k-\frac{r_D}{\left(1-\alpha \right)}-\frac{\partial {C}_k\left({L}_k\right)}{\partial {L}_k}}{r_k}=\left(\frac{\left(1-{\beta}_k\right)}{r_k}\right)\left(\frac{L_0}{N}-\frac{r_kB}{N}\right)\frac{1}{\left(b+\frac{B}{N^2}\right)} $$

The left side of Eq. 17 is the expression of the Lerner index corrected for the risk of insolvency. The right side contains the determinants of market power, which are (a) the risk of default (βk), (b) the average size of an MFI (L0/N), (c) the number of MFIs (N), (d) the elasticity of demand for loans from MFI k (b) which accounts for the MFI’s specialization in a certain financial service, and (e) the total demand elasticity for loans with respect to the average interest rate (B).

Table 4 Translog Cost Results
Table 5 Stochastic Cost Frontier Results
Table 6 Stochastic alternative profit frontier results
Table 7 Endogeneity test and instrumental relevance

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Aguilar, G., Portilla, J. Determinants of Market Power in the Peruvian Regulated Microfinance Sector. J Ind Compet Trade 20, 657–688 (2020).

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  • Microfinance
  • Competition
  • Lerner index
  • Market power

JEL Classification

  • G21
  • L11