ECON 4643: Development Economics

Lecture 3: Credit Markets and Microfinance

Author

Harounan Kazianga
Oklahoma State University
Spring 2024

Code 
if (!require("pacman")) install.packages("pacman")
Loading required package: pacman
Code 
pacman::p_load(haven, DescTools, knitr, kableExtra, ineq, ggplot2, formatdown, tidyverse, WDI, latex2exp, stargazer, lmtest, sandwich)

Reading

  • DR Chapters 14

  • Morduch “The Microfinance Promise”

  • Morduch, J. (2011). Chapter 12: “Does Microfinance Really Help the Poor? New Evidence on Flagship Programs in Bangladesh”. In S. R. Osmani, and M. A. Baqui Kalily (Eds.), Readings in Microfinance: Reach and Impact (pp. 323-349). The working paper version can be downloaded here

Overview

  • Discussions of the next three topics – Rural sector:

    • Financial markets: credit and insurance
    • Farm households
    • Intra-household decision making

  • Also applicable to informal sector analysis

  • Characterized by missing or imperfect markets.

    • Information concerns:

      • Unobserved actions.

      • Unobserved types.

    • Incentive issues:

      • Conflict with insurance (moral hazard).

    • Short-term contracts.

  • Enforcement concerns:

    • Limited Liability.

    • Breaking Agreements.

Credit in Low-Income Settings

  • Most farming households in developing countries have low incomes, and thus have little or no savings. Without savings, two kinds of credit are needed:

    1. Short-term credit to purchase inputs (such as seeds, fertilizer, pesticides, herbicides, hired labor). The loan is repaid at harvest
    2. Long-term credit to:
      1. purchase land
      2. invest in productive capital (tools, machinery, etc.) improve land (irrigation, terracing, etc.)
      3. adopt technology that is risky but, on average, is more productive

  • Unfortunately, often little credit is available in rural areas, and what little there is may be available at high interest rates.

    • The lack of credit is surprising because, on average, the investments that the credit is needed for are very productive

  • Note: the slides on insurance are posted on Canvas.

Source of credit

  1. Private commercial banks. This is pretty rare. One reason, processing costs are large for small loans (as much as 15-40% of the amount lent).
  2. Government banks, especially those whose mandate is to provide credit to agricultural households. This is common in many countries.
  3. Small private moneylenders. These are relatively wealthy people in the community who know a lot about the households they lend to. But they often charge high interest rates. This is very common.
  4. Friends and relatives. This is also common but for many people their friends and relatives don’t have very much money to lend them.

Specific issues of rural credit market

  1. Inherent Risk of Agriculture. Private banks and other private moneylenders are usually in the business to make money, and they can do so only if they are repaid. If they are pretty certain that they will get repaid, they will lend a lot of money, but if they are worried about repayment, they will limit the amounts they lend, usually lending only to low risk borrowers. Because agriculture is often a high-risk activity, lenders will either not make loans to agricultural households, or will lend only small amounts, and at fairly high interest rates.

  2. Lack of Collateral. Lenders want to get repaid (with interest). If they have doubts about getting repaid, they want the borrower to pledge some collateral that they can take if the borrower defaults. But rural households often have very little to offer as collateral. The main thing they may have is land, which they are reluctant to use (because if they lose it they will be in big trouble). In traditional societies where land is allocated by a village leader, the farmer may not have the right to pledge the land as collateral.

Credit Markets

  • Interest rates are high and variable in low-income countries

  • There are several big reasons for this:

    • Limited liability: cannot be compelled to pay back the whole cost of the loan
    • Information issues: adverse selection and moral hazard
    • Enforcement issues: voluntary/involuntary default imperfect competition

  • We will review the theory first, and then we will discuss microfinance

  • This way, it will be more apparent which problems (in theory) microfinance is designed to solve.

Credit Markets: Limited Liability

  • \(L=\) total amount lent out

  • \(r=\) opportunity cost of funds (e.g. the lender could invest in risk-free government bounds that pay interest rate \(r\))

  • \(i=\) interest rate

  • \(p=\) fraction of loan that will be repaid

  • Expected profit \(( E[\pi] )\) is:

\[E\left[ \pi \right] = p\left[L(1+i)-(1+r)L\right]+(1-p)\left[-(1+r)L \right]\]

\[ E\left[ \pi \right] = p\left[(1+i)-(1+r)L \right] \]

\[ E\left[ \pi \right] = L\left[ p(1+i)-(1+r) \right] \]

Assume perfect competition

  • This means that expected profit is zero

  • So, \(p(1+i) = 1+r\), i.e. \(1+i=\frac{1+r}{p}\)

  • \(i=\frac{1+r}{p}-1\)

  • Interest rate \(i\) is decreasing in \(p\), i.e. the interest rate is increasing in \(1-p\), the default rate

  • Example

Code 
library(knitr)
df <- data.frame(
  r = c(0.05, 0.05, 0.05, 0.05, 0.05, 0.05),
  p = c(1, 0.9, 0.8, 0.7, 0.5, 0.3),
  i = c(0.05, 0.167, 0.3125, 0.5, 1.1, 2.5)
)
kable(df, format = "html", booktabs = TRUE, digits=2)
Table 1: Interest rate and default rate, given opportunity cost of funds
r p i
0.05 1.0 0.05
0.05 0.9 0.17
0.05 0.8 0.31
0.05 0.7 0.50
0.05 0.5 1.10
0.05 0.3 2.50

  • The figures in Table 1 assume that lender is risk neutral: if lender is risk averse, \(i\) would be even bigger

  • \(i\) is big because banks must raise rates to deal with high probability of default.

Credit Markets: Moral Hazard

  • Assume that farmer is risk neutral \(u(c)=c\)

  • Incurring effort involves costs \(D\)

  • Probability of payoff \(R\) is \(p\) if he works hard, and \(q<p\) if he does not work hard

  • What if farmer cannot borrow, but can finance himself (he comes up with \(L\) that he could lend to himself at interest rate \(i\))

  • The farmer loses \(L(1+i)\) if crop fails, which is more likely to happen the less hard the famer works

  • Expected utility is:

    • \(p(R-(1+i)L-D)+(1-p)(-(1+i)L-D)\) if works hard, and

    • \(q(R-(1+i)L)+(1-q)(1+i)(-L)\) if does not work hard

  • The farmer works hard if the first quantity is bigger than the second one, or

\[ pR-(1+i)L-D>qR-(1+i)L \]

  • This holds if \(D<(p-q)R\)

    • Interpret this quantity in words

  • Call \(D^{*}_{1}\) the value of \(D\) that makes the farmer exactly indifferent between working hard and slacking, i.e.

\[ D^{*}_{1}=(p-q)R \]

Moral hazard with limited liability

  • Moral hazard: what if the bank cannot observe what people are doing?– cannot tell if someone is working hard or not?

  • Combine this with limited liability: the farmer does not have to pay anything if crop fails

  • Then farmer payoff if he works hard: \(p(R-(1+i)L-D)+(1-p)(-D)\)

  • and if he does not work hard: \(q(R-(1+i)L)\)

  • Now what does the farmer do?

  • Work hard if $ pR-p(1+i)L-D > qR-q(1+i)L $

  • which holds if $ D < (p-q) $

  • Call \(D^{*}_{2}\) the level of effort that makes the farmers indifferent between working hard and slacking under moral hazard, i.e.

\[ D^{*}_{2}=(p-q)[R-(1+i)L] \]

  • Key point (verify that by yourself) \[ D^{*}_{2}<D^{*}_{1} \]

  • We know that the farmer works only if \(D\) is lower than this threshold

  • Hence farmer is less likely to work hard

  • Insight: the farmer still gets payout \(R-L(1+i)\) if his crop is a success, but gets \(0\) instead of \(-L(1+i)\) if his crop is a failure

    -The farmer does not bear the downside risk

    -Therefore the farmer is less concerned about crop failure than he should be and works less hard to avert it.

Possible solutions

  • If the bank had better information, it could simply not pay the farmer if it observes him slacking

  • Use of collateral: farmer must pay back \(C\) when his crop fails

  • Expected utility is now \(p(R-(1+i)L-D)+(1-p)(-C-D)\) if farmers works hard,

  • and \(q(R-(1+i)L)+(1-q)(-C)\) if farmers does not work hard

  • If we set \(C=L(1+i)\), then we get efficient solution- if bank got full collateral, then the problem is solved

  • But… if the farmer had full collateral, why would he go to the bank at the first place?

Microfinance

  • Microfinance is a response to lack of access to credit by poor households

  • Many poor people participate in ROSCAs as a way to save and get access to “credit”

  • But credit itself is very difficult for many to obtain

  • For all the reasons we discussed (adverse selection, moral hazard, contract enforcement, perhaps lack of competition in the banking sector)

  • Microfinance is a method to get credit to low-income individuals, who are usually excluded from the formal credit market

Example: The Grameen Bank

  • The first big microfinance institution was the Grameen Bank, in Bangladesh

  • It was started by Muhammad Yunus, an economist

  • First loan was for $27 to 42 women, in 1974 during a famine

  • Started a formal bank not long thereafter

  • See the 16 decisions

Usual approach

  • The basic idea of microcredit is to give loans in groups (not universal)

  • Strategy varies, but the basic group idea is that failing to repay either prohibits other group members from getting loans, or they have to co-sign for your loan, etc.

  • Typically loans have been targeted to serve a general social purpose - i.e. especially to women, to foster microenterprise, etc.

  • This is not, however, always the case

  • Grameen bank had long reported positive profits, and that it had served this social purpose as well, so that it was basically win-win

  • we will talk a bit about the actual empirics behind it all

  • Basic problem: tradeoff between targeting the very poor and profits, at least empirically

  • Lots of heterogeneity in the types of microfinance banks out there these days.

  • Other issues:

    • What is the impact of microfinance?

    • Who benefits? “rich poor” vs. “poor poor”

The “Standard” Microfinance Model

  • Goal: harness the power of the group structure to overcome hidden information and repayment problems

  • Default is low

  • Loans are often used for investments

  • More focus on women

The Rationale of Group Incentives

  • Say that we have an adverse selection problem (similar to what we saw in the previous lecture)

  • Then, only 1 interest rate can be charged, and it might be too high for the safe types to want to stay in the market

  • In microfinance, borrowers can match into groups.

  • For simplicity, let consider groups of 2

  • Bank can make borrowers pay back \(L(1 + i )\) if they are successful

  • Partner pays \(c\) if they are successful but their partner fails: group liability - both partners are responsible for

  • Which type would people want to match with?

  • All want to match with safe types

  • Would safe type agree to match with risky type?

    • He might if the risky type compensated him

    • But we will see that this won’t happen in a very simple model

  • Also, the \(c\) will likely induce the risky types to pay a higher “effective interest rate”

  • logic: risky types are more likely to fail and so their partners will have to cover them more often

Risky Types

  • Let the probability of success be \(p_{2}\) for a risky type and \(p_{1}\) for a safe type, and \(p_1 > p_2\)

  • If the project is successful, the payoff is \(R_{2}\) for a risky type and \(R_{1}\) for a safe type

  • Let say a risky type is matched with a risky type:

\[\begin{eqnarray*} EU &=& p_{2}\left[R_{2}-L(1+i)-(1-p_{2})c\right] \\ &=& p_{2}R_{2}-p_{2}L(1+i)-p_{2}(1-p_{2})c \end{eqnarray*}\]

  • If a risky type is matched with a safe type, he gets

\[\begin{eqnarray*} EU &=& p_{2}\left[R_{2}-L(1+i)-(1-p_{1})c\right] \\ &=& p_{2}R_{2}-p_{2}L(1+i)-p_{2}(1-p_{1})c \end{eqnarray*}\]

  • So, risky types are better off when they are matched with safe types

Safe Types

  • A safe type matched with a safe type gets

\[ EU=p_{1}R_{1}-p_{1}L(1+i)-p_{1}(1-p_{1})c \]

  • A safe type matched with a risky type gets

\[ EU=p_{1}R_{1}-p_{1}L(1+i)-p_{1}(1-p_{2})c \]

  • Again, safe types are better off when they are matched with safe types

Matching

Risky Types

  • If the system is left alone, a safe type always matches with a safe type and a risky with a risky (why?)

  • Let assume that the risky type could pay a safe type to match with him. How much extra utility does he get out of matching with a safe type, instead of a risky type?

  • Answer: take the difference between risky/safe and risky/risky:

\[\begin{eqnarray*} && p_{2}R_{2}-p_{2}L(1+i)-p_{2}(1-p_{1})c- \\ && \left[p_{2}R_{2}-p_{2}L(1+i)-p_{2}(1-p_{1})c \right]\\ &=&-p_{2}(1-p_{1})c+p_{2}(1-p_{2})c \\ &=&p_{2}c(p_{1}-p_{2}) \end{eqnarray*}\]

  • This the maximum a risky type would pay to match with a safe type

Safe Types

-How much does a safe type lose when he is matched with a risky type?

  • Answer: difference between safe/safe and safe/risky

\[\begin{eqnarray*} && p_{1}R_{1}-p_{1}L(1+i)-p_{1}(1-p_{1})c- \\ && \left[p_{1}R_{1}-p_{1}L(1+i)-p_{1}(1-p_{2})c \right] \\ &=&-p_{1}(1-p_{1})c+p_{1}(1-p_{2})c \\ &=&p_{1}c(p_{1}-p_{2}) \end{eqnarray*}\]

  • This the minimum a safe type would need to agree to match with a risky type

  • So, in order to match with a safe type, a risky type is willing to pay up to \(p_{2}c(p_{1}-p_{2})\)

  • But in order to match with a risky type, a safe type needs to be compensated by at least \(p_{1}c(p_{1}-p_{2})\)

  • The second quantity is bigger because \(p_{1}>p_{2}\)

  • Implication: the safe type needs more than the risky type can pay

    • A safe type matched with a risky type has to pay for his partner very commonly (i.e. the probability that he is successful and his risky partner is unsuccessful is high)

    • But a risky type matched with a risky type has to pay for his partner less often (i.e. the probability that he.s successful and his risky partner is unsuccessful is lower, since he.s not as likely to be successful)

    • Conclusion: safe matches w/ safe, risky w/ risky (positive matching)

Effective interest rate

  • So, how much do people pay (in expectations) in insuring their partner?

  • risky-risky: \(p_{2}(1-p_{2})c\)

  • safe-safe: \(p_{1}(1-p_{1})c\)

  • Numerical illustration: let say \(p_{1}=0.9\) and \(p_{2}=0.8\)

    • \(p_{1}(1-p_{1})=0.9*0.1=0.09\)

    • \(p_{2}(1-p_{2})=0.8*0.2=0.16\)

    • risky-risky pays more than safe-safe

  • In general, if \(p_{1}>p_{2}>0.5\), then risky-risky always pays more

Hidden Information and Enforcement Problems

  • Similarly the \(c\) can tend to impede moral hazard so long as there is some monitoring between parties

  • Idea: gives an incentive to keep an eye on your partner

  • Other things the bank can do

    • offer a dynamic repayment incentive: if borrower does not pay back, he is barred from all future loans

    • Regular repayment rather than fixed repayment at the end of the term as is usually the case

    • Require collateral, or require to save on top of the repayment, etc.

Does Microfinance Really Help the Poor?

  • Microfinance is a really wonderful concept and an incredibly important way to target poor people.

  • Many unanswered questions, however:

    • What outcomes are we interested in? Poverty? Small business development? Female empowerment issues?

    • Does microfinance help the poor poor or the rich poor? How do we think about MF if it is the rich poor? Is it “bad” if MF helps only the relatively better off?

  • Most importantly: what is the impact of microfinance, on any dimension?

Does Microfinance Really Help the Poor?– A Case Study}%

  • 1800 observations for 87 villages in 29 tanas (districts) in Bangladesh

  • Some have Microfinance programs, some do not

  • 3 programs: Grameen, BRAC (Bangladeshi rural advancement committee), BRDB (Bangladesh rural development board)

  • These programs located in certain villages (non-randomly)

  • Think about how we can estimate a program effect.

  • The evaluation is going to be based on the fact that the programs were only supposed to make loans to people with less than 0.5 acres of land. People with more than 0.5 acres were not supposed to be targeted by these programs.

  • Morduch uses a technique difference-in-difference

Key finding

  • Microfinance seemed to have a relatively lower impact on consumption

  • These results are in stark contrast to some earlier work with similar data by Pitt and Khandker (1998). They find large impacts for women.

  • Possible reasons:

    • Rules do not seem to be enforced.

    • Perhaps you get into the program if you are poor

    • OR the program officer likes you.

    • Obviously this is going to bias the results significantly lots and lots of mistargetting here makes it very hard to know what the true results were

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