Market power, social welfare, and efficiency in the Peruvian microfinance

Abstract

This study quantifies the social welfare loss caused by market power in Peru’s regulated microfinance industry and analyzes its effect on microfinance institutions’ (MFIs) efficiency from 2003 to 2019. We estimate the efficiency-adjusted Lerner index as a measure of market power and obtain efficiency scores via cost and profit stochastic frontiers estimation using data from a wide panel of MFIs. Additionally, to analyze the effect of market power on the MFI’s efficiency, we estimate a fixed effects model with instrumental variables to correct the endogeneity problem. The results show that the welfare loss due to market power in Peru’s regulated microfinance industry has increased from 0.12% of GDP in 2003 to 0.27% in 2019. It is also found that market power positively affects Peruvian MFIs’ efficiency. Therefore, reducing market power leads to a welfare gain by lowering the social welfare loss (Harberger’s triangle) and a welfare loss due to decreased efficiency in MFIs. However, we find that reducing market power leads to a positive net effect on social welfare due to greater welfare gain than loss.

Appendix

• 1. Harberger’s triangle

An MFI with market power in the microcredit market maximizes its profit by choosing the price or interest rate (P) that it will charge for its loans (L). The problem to be solved is therefore:

$$Max \pi \left(L\right)=P\left(L\right)L-TC\left(L\right)$$

(12)

The first-order condition to solve this problem is:

$$\frac{\partial \pi }{\partial L}=\frac{\partial P\left(L\right)}{\partial L}L+P\left(L\right)-\frac{\partial TC}{\partial L}=0$$

$$P\left(L\right)-\frac{\partial TC}{\partial L}=-\frac{\partial P\left(L\right)}{\partial L}L$$

$$P\left(L\right)-\frac{\partial TC}{\partial L}=-\frac{\partial P\left(L\right)}{\partial L}L\frac{P}{P}$$

$$\frac{P\left(L\right)-\frac{\partial TC}{\partial L}}{P}=-\frac{1}{\frac{\partial L}{\partial P}\frac{P}{L}}=-\frac{1}{\varepsilon }$$

(13)

Since $\frac{\partial TC }{\partial L}$ is the marginal cost (MC), the term on the left of Eq. (13) is the Lerner index (LI) and $\frac{\partial L}{\partial P}\frac{P}{L}$ is the price elasticity of loans demand (ɛ). Therefore, we obtain from profit maximization:

$$LI=-\frac{1}{\varepsilon }$$

(14)

The net loss of social welfare in Fig. 1 is equivalent to the area of triangle ABC:

$$\Delta ABC=\frac{\left({P}^{*}-MC\right)\left({L}_{PC}-{L}^{*}\right)}{2} =\frac{1}{2}\frac{\left(MC-{P}^{*}\right)\left({L}_{PC}-{L}^{*}\right)}{\left(MC-{P}^{*}\right)}\frac{\left({P}^{*}-MC\right){P}^{*}{L}^{*}}{{P}^{*}{L}^{*}}$$

$$\Delta ABC=-\frac{1}{2}\frac{\left({L}_{PC}-{L}^{*}\right)}{\left(MC-{P}^{*}\right)}\frac{{P}^{*}}{{L}^{*}}\frac{{\left({P}^{*}-MC\right)}^{2}{L}^{*}}{{P}^{*}}=-\frac{1}{2}\varepsilon \frac{{\left({P}^{*}-MC\right)}^{2}{L}^{*}}{{P}^{*}}$$

Replacing ɛ from Eq. (14), we have:

$$\Delta ABC=-\frac{1}{2}\left[-\frac{1}{LI}\right]\frac{{\left({P}^{*}-MC\right)}^{2}{L}^{*}}{{P}^{*}}$$

Replacing LI by $\frac{{P}^{*}\left(L\right)-MC}{{P}^{*}}$, we have:

$$\Delta ABC=\frac{1}{2}\left[\frac{({P}^{*}-MC)}{{P}^{*}}\right]{P}^{*}{L}^{*}=\frac{1}{2}LI({P}^{*}{L}^{*})$$

See Table 6, 7, 8, 9, 10, 11 and 12.

Table 6 Definitions of variables and indicators

Table 7 Descriptive statistics

Table 8 Stochastic cost frontier results

Table 9 Stochastic alternative profit frontier results

Table 10 First stage of IV with fixed effects estimation

Table 11 Robustness analysis: stochastic alternative profit frontier results

Table 12 Robustness analysis: social welfare loss, weighted averages cost and profit efficiencies, and social costs associated with cost and profit inefficiency. In addition, variation in welfare loss associated with reduced cost efficiency and profit efficiency from a 10% reduction in market power (% GDP)