Building Credit Histories with Heterogeneously-Informed Lenders

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1 Building Credit Histories with Heterogeneously-Informed Lenders Natalia Kovrijnykh Arizona State University Igor Livshits University of Western Ontario Ariel Zetlin-Jones CMU - Tepper June 28, 2017

2 Motivation Credit histories determine consumer access to credit We explore a particular mechanism of credit-history building Heterogeneously-informed lenders use credit histories to aggregate information about a consumer s creditworthiness Borrowers take on loans to facilitate information aggregation - i.e. build credit history through taking on loans Mechanism distinct from building credit history through repaying How does taking out a loan affect future credit terms? Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 1 / 17

3 What We Do Develop a simple dynamic model with risky borrowers and heterogeneously-informed lenders Credit-history building = information aggregation across lenders Borrowers take loans from a positively-informed lender to signal their credit worthiness to other lenders Costs of building a credit history to high-quality borrowers: Cross subsidization Excessive borrowing Novel insight into debt dilution: more dilution is better For a borrower of a given quality/risk, larger loan increases the probability of default But larger loans are taken out by less risky borrowers Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 2 / 17

4 Environment

5 Model Two periods, 1 and 2; period 1 has two stages, I and II lending over the two stages of period 1 repayment/default in period 2 Borrowers (one or many) Risk averse Endowment in period 1: fixed, low Endowment in period 2: uncertain - Support: {e l, e m, e h } - State s {g, b} borrower is either good or bad - Pr(e = e l s = g) = 0, Pr(e = e h s = b) = 0 - Borrower is good with probability α Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 3 / 17

6 Information Structure Lenders (many, partitioned into two blocks) Risk neutral Each receives a private signal about the borrower s state Within each block, lenders observe the same signal σ {P, N} Pr(σ = P s = g) = Pr(σ = N s = b) = (1 + ρ)/2, where ρ (0, 1] Signals across the blocks are conditionally independent Lenders information in stage II of period 1 Signal from stage I Borrower s credit history from stage I (to be defined...) Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 4 / 17

7 Actions In each stage of period 1 Lenders offer contracts: (loan size, price)=(x, q) Borrower accepts one or none of the offered contracts in each stage The terms of the accepted contract are publicly observed Credit history in stage I: Credit history in stage II: accepted (x, q) from stage I (if any) In period 2 After observing endowment e j, borrower chooses to repay or default If default, consumes (1 ϕ)e j - ϕe j is the dead-weight loss of bankruptcy For the talk, restrict borrower s loan balance {ϕe L, ϕe M, ϕe H } small, medium, large loan Notice that the smallest loan ϕe L is riskless as everyone repays it Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 5 / 17

8 Equilibrium

9 Equilibrium Concept Perfect Bayesian Equilibrium (PBE) in pure strategies Require beliefs to satisfy the Cho-Kreps intuitive criterion Standard way to eliminate multiplicity of equilibria in signaling games Result: There is a unique equilibrium outcome Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 6 / 17

10 Results

11 Equilibria and Information Aggregation Assumption Equilibrium loan size without info is > ϕe l Rules out equilibrium where everyone borrows φe l at risk-free rate Claim Any PBE that satisfies the intuitive criterion features information aggregation The claim means that there are no equilibria where no lender makes an offer in stage I all lenders make the same offer in stage I This means that in equilibrium, some lenders make offers in stage I borrowers learn both signals (their types ) from observing offers at least some (types of) borrowers accept offers lenders whose offers were not accepted (or who did not make offers) learn the borrower s type from the contract he accepts Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 7 / 17

12 Information Aggregation = Credit History Building Suppose only P-lenders make offers, and they offer small loans Borrowers with two offers (PP) want to aggregate this info P-lender whose offer they don t accept may want to lend more We interpret taking an early loan with the purpose of aggregating information as credit history building Borrowers with one offer (PN) don t benefit from info aggregation They have no need to let an N-lender know there is a P-lender - Borrowing from an N-lender who knows the other signal is P is the same as borrowing from a P-lender who knows the other signal is N PNs might take out an early loan too, but not to build credit history, only to free-ride on a better, cross-subsidized price Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 8 / 17

13 How Can Equilibria Look? 1. With cross subsidization (both PPs and PNs accept stage-i loan) a) Loan-size separation: in stage II, PP, PN, NN get different-size loans b) Pooling of PP and PN on loan size: PP, PN get same loan, different prices; NN gets same loan at lower price, or smaller loan 2. Without cross subsidization (only PPs accept stage-i loan) a) Full separation: in stage II, PP, PN, NN get different-size loans b) Separation of PP and PN: in stage II, PP gets different loan from PN and NN, who get same, risk-free loan Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 9 / 17

14 Costs of Credit-History Building Costs of credit-history building (to PP-borrowers): Cross-subsidization PP-borrowers may cross-subsidize PN-borrowers Excessive Borrowing Happens when PP-borrowers end up with a large loan, while under full info they would get a medium loan Result: PP-borrowers prefer costly information aggregation to no information aggregation The intuitive criterion picks PP s favorite equilibrium Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 10 / 17

15 Zoom In: Particular Equilibrium Illustrate both costs Derive the more-dilution-is-better result

16 Example of Equilibrium with Both Costs Loan-size separation with cross subsidization In stage I, All lenders with P signals offer a small loan All borrowers with such offers accept one In stage II, P-lenders whose offer wasn t accepted, top up PPs to a large loan Either P- or N-lenders top up PNs to a medium loan NN-borrowers receive a small loan Price of stage-i loan: q P = Pr(PP P)q H PP + Pr(PN P)qM PN where q H PP = Pr(repaying large loan PP)/(1 + r f ) q M PN = Pr(repaying medium loan PN)/(1 + r f ) Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 11 / 17

17 Cross Subsidization in the Example Equilibrium Condition for cross subsidization: PN-borrower prefers to accept the stage-i offer when or q P > q M PN or q H PP > qm PN Pr(repaying large loan PP) > Pr(repaying medium loan PN) ( ) Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 12 / 17

18 Excessive Borrowing in the Example Equilibrium Suppose in a full-info benchmark, PP-borrowers would get a medium loan Why do PPs get a large loan in the example equilibrium? Suppose both PP are PN topped up to a medium loan in stage II (at different prices) On the stage-i small loan, PPs still cross subsidize PNs So PPs get the medium loan, but not at the price of the full-info benchmark Given the worse, cross-subsidizing prices, PPs might prefer a large loan to a medium loan Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 13 / 17

19 More Dilution is Better In the example equilibrium, there is uncertainty for the stage-i lender about how much he will get diluted in stage II Result: The incumbent is more likely to be repaid if he is diluted by more PPs dilute to a large loan PNs dilute to a medium loan Condition for cross-subsidization: Pr(repaying large loan PP) > Pr(repaying medium loan PN) ( ) Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 14 / 17

20 More Dilution is Better The result is contrary to the conventional wisdom that more dilution increases the probability of default i. For a borrower of a given quality/risk, larger loan increases the probability of default ii. But here, less risky borrowers take out larger loans Selection effect (ii.) dominates the dilution effect (i.) In all other equilibria there is no heterogeneity in dilution Information aggregation is key for this result: a larger top-up loan conveys positive information of the diluting lender Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 15 / 17

21 Comparative Statics

22 Comparative Statics wrt Signal Precision ρ More dilution is better Cross Subsidization Yes Yes No Yes Yes Excessive Borrowing No No Yes Yes No Equilibrium Outcome m m m l m m l m h Symm. Info Outcome 0 1 m m m l m m l m h ρ Notation: lmh means ϕe l to NN, ϕe m to PN, ϕe h to PP One robust prediction: more dilution is better This result is at play for high values of signal precision Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 16 / 17

23 Conclusions Develop a model of credit-history building by taking out loans Credit-history building = information aggregation Costs of credit-history building Cross subsidization Excessive borrowing Novel insight into debt dilution Larger dilution loan is good news for the incumbent lender Work in progress Obtaining credit-report data to test key model predictions Kovrijnykh, Livshits, & Zetlin-Jones Building Credit Histories 17 / 17