Microfinance Markets Reference: Irfan-Ortiz (2014) Microfinance - - PDF document

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Microfinance Markets Reference: Irfan-Ortiz (2014) Microfinance - - PDF document

Sep 16, 2022 175 likes •332 views

5/1/17 Microfinance Markets Reference: Irfan-Ortiz (2014) Microfinance Market Interventions The story of microfinance 1 5/1/17 Story of microfinance movement 1970s to today Story of microfinance movement 2 5/1/17 Story of microfinance

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Microfinance Markets

Reference: Irfan-Ortiz (2014)

Microfinance Market Interventions

The story of microfinance

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Story of microfinance movement

— 1970s to today

Story of microfinance movement

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Story of microfinance movement

  • Dr. Muhammad

Yunus

Congressional Gold Medal (2013) Nobel Peace Prize (2006)

Loan without collateral!

— Yet very low default rate — What makes it work:

  • Group lending with joint-liability contract
  • Group lending mitigates "moral hazard"

– Also reduces monitoring costs

  • Assortative matching mitigates "adverse selection

problem"

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Interest rates

— Not "weapon for competition" among banks

(Porteous, 2006)

— Other factors

  • Loan size
  • Shorter waiting period
  • Flexibility in repayment
  • Savings account
  • Health care

More on microfinance

— The Economics of Microfinance

(Armendariz and Morduch, 2010)

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What do we want to do?

— Model microfinance markets — Goal: assist policy makers

Questions

  • Shut down loss-making banks?
  • Set a cap on interest rates?
  • Subsidize banks?

Causal Strategic Inference (CSI)

— Causal probabilistic inference (Judea Pearl)

  • Prediction
  • Intervention
  • Counterfactual

— Interventions in game-theoretic settings

  • Set the actions of certain players

(Irfan & Ortiz, AI Journal, 2014)

  • Change the structure of the game (this work)

Modeling Learning Computation

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Our model of microfinance market

— MFIs want

  • Set interest rates s.t. supply = demand

— Villages want

  • Maximize amount of loan s.t. repayment

Banks/MFIs Villages

Equilibrium

✔

Related: Graphical Economics (Kakade, Kearns, & Ortiz, 2004) Diffusion of Microfinance (Jackson et al., 2013) MFI = Microfinance institution

Learning, Computation, Intervention

— Data: Bangladesh and Bolivia

Example of Intervention: Shut down a loss-making bank

1

Learn parameters before intervention Learning method: bi-level optimization

2

Compute equilibrium: iterative algorithm

3

Remove the bank from model

4

Compute equilibrium again

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Model of microfinance market

j k i xji Ti ri Banks/MFIs Villages

Amount of Loan Revenue generated

j k [slope: ek] dk

Model of microfinance market

Nash Equilibrium: <interest rates, allocations>

  • 1. MFI side is satisfied
  • 2. Village side is optimized

MFI side Village side Market clearance

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Special case: no diversification (λ = 0)

— Assume:

Villages have the same revenue function

— Equilibrium point exists; unique interest rates

  • Proof: Equivalent Eisenberg-Gale convex program
  • Polynomial-time algorithm to compute an equilibrium

[Vazirani, 07]

General case

— An equilibrium point exists

  • Constructive proof: Use properties of strategic

complementarity and strategic substitutability

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Algorithm for equilibrium computation Using the model in the real world

— Data from Bangladesh and Bolivia

MFIs Villages

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Estimating model parameters

— Problem

  • Learn the parameters from data
  • Capture (approximately) the real-world scenario as a Nash

equilibrium — Solution approach

  • Optimization

j k i xji Ti ri

Amount of Loan Revenue generated

j k [slope: ek] dk

Optimization in machine learning

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Equilibrium vs. observed allocations (Bolivia)

5000 10000 15000 20000 25000 30000 35000 40000 45000 5000 10000 15000 20000 25000 30000 35000 40000 45000

Equilibrium Loan Allocations Observed Loan Allocations

Observations

— Bias vs. variance

  • Does not overfit

— Equilibrium selection

  • Robust in the presence of noise
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Bias vs. variance

— Add noise to data è Training set — Calculate equilibrium — Distance to observation è Test error

Bias vs. variance

— Gaussian noise model

0.05 0.052 0.054 0.056 0.058 0.06 0.062 0.064 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Average Relative Deviation Noise Level Training error Test Error

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What do we want to do?

— Model microfinance markets — Goal: assist policy makers

Causal Strategic Inference (CSI) Questions

  • Shut down loss-making MFIs?
  • Set a cap on interest rates?
  • Subsidize banks?

Shut down loss-making MFIs

2 4 6 8 10 12 14 16 1 2 3 4 5 6 7

Interest Rates MFIs Observed interest rates Learned interest rates Equilibrium interest rates

BRDB PDBF BRAC ASA PKSF GRAM Other

Competition vs. interest rates [D. Porteous, 2006]

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Cap on interest rates

2 4 6 8 10 12 14 16 1 2 3 4 5 6 7

Interest Rates MFIs Observed interest rates Learned interest rates Equilibrium interest rates

13.4975%

[July 2011] Cap on interest rates 13.5%

BRDB PDBF BRAC ASA PKSF GRAM Other

Role of subsidies

21 22 23 24 25 26 1 2 3 4 5 6 7 8

Interest Rates MFIs Before giving subsidies After giving subsidies

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Other inference questions

— New branches — How to make loans more affordable by

subsidies

— Major bank going out of business

In brief…

— Model microfinance markets — Learn the parameters — Answer CSI questions — Extensions (with Lucy Luo & Marcus Christiansen)

  • Diminishing marginal returns on investing loan
  • Model village side preference
  • Model group lending
  • Consider MFI-level characteristics

Economics Machine Learning Algorithms