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

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 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" 3

5/1/17 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) 4

5/1/17 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 5

5/1/17 Our model of microfinance market MFI = Microfinance institution Banks/MFIs Villages ✔ Equilibrium — MFIs want ◦ Set interest rates s.t. supply = demand — Villages want ◦ Maximize amount of loan s.t. repayment Related: Graphical Economics (Kakade, Kearns, & Ortiz, 2004) Diffusion of Microfinance (Jackson et al., 2013) Learning, Computation, Intervention — Data: Bangladesh and Bolivia Example of Intervention: Shut down a loss-making bank Learn parameters before intervention 1 Learning method: bi-level optimization 2 Compute equilibrium: iterative algorithm 3 Remove the bank from model 4 Compute equilibrium again 6

5/1/17 Model of microfinance market T i Banks/MFIs i r i x ji Villages j k Revenue generated j k [slope: e k ] d k Amount of Loan Model of microfinance market Market clearance MFI side Nash Equilibrium: <interest rates, allocations> 1. MFI side is satisfied 2. Village side is optimized Village side 7

5/1/17 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 8

5/1/17 Algorithm for equilibrium computation Using the model in the real world — Data from Bangladesh and Bolivia MFIs Villages 9

5/1/17 Estimating model parameters — Problem ◦ Learn the parameters from data ◦ Capture (approximately) the real-world scenario as a Nash equilibrium T i i r i — Solution approach x ji ◦ Optimization j k Revenue generated j k [slope: e k ] d k Amount of Loan Optimization in machine learning 10

5/1/17 Equilibrium vs. observed allocations (Bolivia) 45000 40000 35000 Equilibrium Loan Allocations 30000 25000 20000 15000 10000 5000 0 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 Observed Loan Allocations Observations — Bias vs. variance ◦ Does not overfit — Equilibrium selection ◦ Robust in the presence of noise 11

5/1/17 Bias vs. variance — Add noise to data è Training set — Calculate equilibrium — Distance to observation è Test error Bias vs. variance — Gaussian noise model 0.064 0.062 Training error Test Error Average Relative Deviation 0.06 0.058 0.056 0.054 0.052 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Noise Level 12

5/1/17 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 Competition vs. interest rates 16 [D. Porteous, 2006] Observed interest rates Learned interest rates 14 Equilibrium interest rates 12 Interest Rates 10 8 6 4 2 0 1 2 3 4 5 6 7 MFIs BRAC ASA PKSF GRAM BRDB PDBF Other 13

5/1/17 Cap on interest rates 16 Observed interest rates 13.4975% Learned interest rates 14 Equilibrium interest rates 12 Interest Rates 10 [July 2011] 8 Cap on interest 6 rates 13.5% 4 2 0 1 2 3 4 5 6 7 MFIs BRAC ASA PKSF GRAM BRDB PDBF Other Role of subsidies 26 Before giving subsidies 25 After giving subsidies Interest Rates 24 23 22 21 1 2 3 4 5 6 7 8 MFIs 14

5/1/17 Other inference questions — New branches — How to make loans more affordable by subsidies — Major bank going out of business In brief… — Model microfinance markets Economics — Learn the parameters Machine Learning — Answer CSI questions Algorithms — Extensions (with Lucy Luo & Marcus Christiansen) ◦ Diminishing marginal returns on investing loan ◦ Model village side preference ◦ Model group lending ◦ Consider MFI-level characteristics 15