Abstract
We analyse equilibrium borrowers’ effort and the cost of microcredit loans in the presence of moral hazard, project correlation and subsidies under group lending conditions. Our results show that under the assumption of endogenous effort, project correlation has significant effects on borrowers’ effort only when it is determined by asymmetric (positive or negative) shocks. These findings indicate that the well-known negative effect of within-group (symmetric) project correlation on group lending with joint liability disappears once endogenous effort is taken into account. We also analyse the effects of subsidised lending (and asymmetric correlation) on the relative convenience (in terms of borrowers’ effort) of the alternative (1) between group lending and individual lending with notional collateral and (2) among three different market structures of the microfinance industry.
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Notes
As an idea of what small loans can mean, in his first experiment Yunus remembers that in 1976 with 27 dollars he could lend to 42 bamboo workers who needed 22 cents each to buy raw material for their work.
Even though strongly supported by economists, this interpretation cannot explain all of microfinance’s success. This is because some successful MFIs (including Grameen after its 2000 reform and the start of the Grameen II system) do not use joint liability. Another interpretation, related to the existing literature on small firm financing, is that of relationship banking. As is well known, Berger and Udell (2002) emphasise the key role of loan officers who accumulate “soft” information, crucial to assess creditworthiness of small businesses. One of the main characteristics of microfinance is the higher capacity of accumulating soft information (especially when operating at village level) and the relatively low ratio of borrowers per staff members (averaging around 120 in the group of MFIs surveyed by the MicroBanking Bulletin). It should be noted that a further novel feature of microfinance is that its bank officers act not just as external monitors, but contribute to the borrowers’ training. In the example of the Grameen Bank, borrowers are offered periodical meetings to develop their entrepreneurial skills as a means of increasing the probability of their economic survival. In this way MFIs seem to be aware that success in small business activity is dependent on human capital formation and not just on bridging a funding gap (Cressy 1996).
Since we assume that borrowers cooperate with each other, the analysis of a single borrower applies symmetrically to the other. Hence both will solve their problem in the same way and independently choose the same level of effort, p.
Cooperative effort implies that the two groupmates or co-borrowers act accordingly. This occurs when deviations from the commonly chosen behavior are not convenient (or not possible) for individual borrowers due to: (1) individual moral beliefs; (2) social sanctions or (3) costless monitoring and enforcement of the chosen effort strategy among groupmates.
When we explore boundaries of the interior solution we find that \( p_{GL\left( \theta \right)} = 1 \) if \( \left( {\gamma - X} \right) = c - R \). Moreover, \( p_{GL\left( \theta \right)} < 1 \) if \( \left( {\gamma - X} \right) > c - R \) and \( p_{GL\left( \theta \right)} > 0 \) holds when \( X > 0 \) and \( \gamma > c \), since \( {{X + \sqrt {X^2 - 4R\left( {\gamma - c} \right)} } \mathord{\left/ {\vphantom {{X + \sqrt {X^2 - 4R\left( {\gamma - c} \right)} } {2\left( {\gamma - c} \right)}}} \right. \kern-\nulldelimiterspace} {2\left( {\gamma - c} \right)}} \) is always positive for real solutions, when \( X \ge 2\sqrt {R\left( {\gamma - c} \right)} \). Finally, \( p_{GL\left( \theta \right)} \le 0 \) is not feasible if we exclude imaginary solutions or negative values of X. Hence, \( \gamma > 0 \), \( X > 0 \), \( R > 0 \), \( \gamma > X > R > c > 0 \) are sufficient conditions for interior optima.
Remember that γ > 2c is a necessary condition to have positive utility.
The total amount due to the bank by one of the two borrowers is paid only in case of the good outcome of his project and therefore may be considered, following Ghatak and Guinnane (1999), as a “tax on success”.
Since these terms are probabilities the following conditions, \( p + \theta _\alpha \le 1 \) and \( p + \theta _\beta \ge 0 \), need to be satisfied in order to have interior solutions.
Consider that we need \( X \ge \frac{{2\sqrt {R\left( {\gamma - c} \right)} }}{{1 + \theta _\alpha - \theta _\beta }} \) for real solutions, \( p_{GL\left( {\theta _\alpha ,\theta _\beta } \right)} > 0 \) always positive for real solutions and \( p_{GL\left( {\theta _\alpha ,\theta _\beta } \right)} \le 1 \) when \( X \le \frac{{\gamma - c + R}}{{1 + \theta _\alpha - \theta _\beta }} \).
We neglect here the impact of the two market structures on the total volume of credit disbursed.
A close inspection of (23’) shows that borrower effort is increasing in (a). Note also that the borrower’s subjective discount rate (1/d) and the probability of getting credit in the second round (v) affect effort only when a > 1.
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Becchetti, L., Pisani, F. Microfinance, subsidies and local externalities. Small Bus Econ 34, 309–321 (2010). https://doi.org/10.1007/s11187-008-9125-y
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DOI: https://doi.org/10.1007/s11187-008-9125-y