Credit Enforcement Cycles Lukasz A. Drozd 1 Ricardo Serrano-Padial 2 - - PowerPoint PPT Presentation

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Credit Enforcement Cycles Lukasz A. Drozd 1 Ricardo Serrano-Padial 2 - - PowerPoint PPT Presentation

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Credit Enforcement Cycles Lukasz A. Drozd 1 Ricardo Serrano-Padial 2 1 FRB Philadelphia 2 Drexel University July, 2017 The views expressed in this paper are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of

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SLIDE 1

Credit Enforcement Cycles

Lukasz A. Drozd1 Ricardo Serrano-Padial2

1FRB Philadelphia 2Drexel University

July, 2017 The views expressed in this paper are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of Philadelphia or the Federal Reserve System.

Drozd and Serrano-Padial: Credit Enforcement Cycles

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SLIDE 2

Drozd and Serrano-Padial: Credit Enforcement Cycles

NEW YORK (CNNMoney, 2012) – Borrowers facing foreclosure are learning that they can stay in their homes for years (...) Among the tactics: Challenging the bank’s actions, waiting to file paperwork right up until the deadline, requesting the lender dig up original paperwork or, in some extreme cases, declaring

  • bankruptcy. Nationwide, the average time it takes to process a foreclosure has

climbed to 674 days from 253 days just four years ago (...).

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SLIDE 3

Drozd and Serrano-Padial: Credit Enforcement Cycles

Credit supply (borrowing constraints/ credit spreads)

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SLIDE 4

Drozd and Serrano-Padial: Credit Enforcement Cycles

Credit supply (borrowing constraints/ credit spreads) Default decisions + Ability to enforce repaym ent / seize collateral

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SLIDE 5

Drozd and Serrano-Padial: Credit Enforcement Cycles

Credit supply (borrowing constraints/ credit spreads) Default decisions + Ability to enforce repaym ent / seize collateral Endogenous to econom ic environm ent:

  • 1. Current and future econom ic conditions
  • 2. Efficacy of enforcem ent institutions
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SLIDE 6

Drozd and Serrano-Padial: Credit Enforcement Cycles

Credit supply (borrowing constraints/ credit spreads) Default decisions + Ability to enforce repaym ent / seize collateral Endogenous to econom ic environm ent:

  • 1. Current and future econom ic conditions
  • 2. Efficacy of enforcem ent institutions

Literature =>

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SLIDE 7

Drozd and Serrano-Padial: Credit Enforcement Cycles

Credit supply (borrowing constraints/ credit spreads) Default decisions + Ability to enforce repaym ent / seize collateral Endogenous to econom ic environm ent:

  • 1. Current and future econom ic conditions
  • 2. Efficacy of enforcem ent institutions

This paper => Literature =>

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SLIDE 8

Motivation

Drozd and Serrano-Padial: Credit Enforcement Cycles

  • 1. Enforcement of credit contracts a time consuming process
  • enforcement of contracts (OECD high-income) 532 days (WB,2017)
  • resolution of insolvency in OECD high-income: 432 days (WB, 2017)
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SLIDE 9

Motivation

Drozd and Serrano-Padial: Credit Enforcement Cycles

  • 1. Enforcement of credit contracts a time consuming process
  • enforcement of contracts (OECD high-income) 532 days (WB,2017)
  • resolution of insolvency in OECD high-income: 432 days (WB, 2017)
  • 2. Widespread defaults lead to major enforcement delays
  • US (06-09): foreclosure timelines 8 ↑ 15 months (Calem, 2014)
  • Italy (07-11): loan enforcement 4 ↑ 6+ years (Bank of Italy, 2014)
  • Spain(07-15): commercial loan enforcement 2.5 ↑ 5 years (est.)
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SLIDE 10

Motivation

Drozd and Serrano-Padial: Credit Enforcement Cycles

  • 1. Enforcement of credit contracts a time consuming process
  • enforcement of contracts (OECD high-income) 532 days (WB,2017)
  • resolution of insolvency in OECD high-income: 432 days (WB, 2017)
  • 2. Widespread defaults lead to major enforcement delays
  • US (06-09): foreclosure timelines 8 ↑ 15 months (Calem, 2014)
  • Italy (07-11): loan enforcement 4 ↑ 6+ years (Bank of Italy, 2014)
  • Spain(07-15): commercial loan enforcement 2.5 ↑ 5 years (est.)
  • 3. Numerous micro-level studies now document causal link to credit
  • court conjestion ⇒ efficacy of enforcement (Iverson, 2015)
  • efficacy of enforcement ⇒ strategic default (Schianterlli, 2016)
  • court conjestion ⇒ cedit supply (Japelli et al., 2005; Safavian and Sharma,

2007; Ponticelli, 2015; Rodano, 2016; Chan et al., 2014):

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SLIDE 11

Motivation

Drozd and Serrano-Padial: Credit Enforcement Cycles

  • 1. Enforcement of credit contracts a time consuming process
  • enforcement of contracts (OECD high-income) 532 days (WB,2017)
  • resolution of insolvency in OECD high-income: 432 days (WB, 2017)
  • 2. Widespread defaults lead to major enforcement delays
  • US (06-09): foreclosure timelines 8 ↑ 15 months (Calem, 2014)
  • Italy (07-11): loan enforcement 4 ↑ 6+ years (Bank of Italy, 2014)
  • Spain(07-15): commercial loan enforcement 2.5 ↑ 5 years (est.)
  • 3. Numerous micro-level studies now document causal link to credit
  • court conjestion ⇒ efficacy of enforcement (Iverson, 2015)
  • efficacy of enforcement ⇒ strategic default (Schianterlli, 2016)
  • court conjestion ⇒ cedit supply (Japelli et al., 2005; Safavian and Sharma,

2007; Ponticelli, 2015; Rodano, 2016; Chan et al., 2014):

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SLIDE 12

Weighted Caseload per Judge in the U.S. (Iverson, 2015)

Drozd and Serrano-Padial: Credit Enforcement Cycles

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SLIDE 13

Weighted Caseload per Judge in the U.S. (Iverson, 2015)

Drozd and Serrano-Padial: Credit Enforcement Cycles

Caseload increases by 30%+ during recessions

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SLIDE 14

Diff-and-Diff BAPCPA Results (Iverson, 2015)

Drozd and Serrano-Padial: Credit Enforcement Cycles

Business cycle 300h extra caseload per judge associated with:

  • probability of ch.11 bankruptcy filing dismisal up by 8%, conversions to

ch.7 up by 11% for SME

  • increased loan losses on C&I up by ≈ 50%
  • re-filing of dismissed cases doubles (recidivism)
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SLIDE 15

What We Do

Drozd and Serrano-Padial: Credit Enforcement Cycles

Build a model of credit supply in which enforcement is a depletable resource

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What We Do

Drozd and Serrano-Padial: Credit Enforcement Cycles

Build a model of credit supply in which enforcement is a depletable resource Use the model to inspect the mechanism:

shock ↑ ⇒ enforcement ↓ ⇒ default ↑ ⇒ credit ↓ ...

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SLIDE 17

What We Do

Drozd and Serrano-Padial: Credit Enforcement Cycles

Build a model of credit supply in which enforcement is a depletable resource Use the model to inspect the mechanism:

shock ↑ ⇒ enforcement ↓ ⇒ default ↑ ⇒ credit ↓ ...

Contribution: analysis of enforcement externality with credit & heterogenious agents in GG-setup

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SLIDE 18

Related Literature

Drozd and Serrano-Padial: Credit Enforcement Cycles

Enforcement externality:

  • Bond and Rai (2009), Arellano and Kocherlakota (2009), tax evasion

and crime literature. Global Games

  • Carlsson and Van Damme (1993), Morris and Shin (1998, 2003),

Frankel, Morris and Pauzner (2003), Sakovics and Steiner (2012)

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SLIDE 19

Model

Drozd and Serrano-Padial: Credit Enforcement Cycles

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SLIDE 20

Model

Drozd and Serrano-Padial: Credit Enforcement Cycles

Two agents (a la Gale and Hellwig, 1985):

Entrepreneurs:

  • seek loans to finance idea/project

Lenders:

  • provide funds subject to zero profits
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SLIDE 21

Model

Drozd and Serrano-Padial: Credit Enforcement Cycles

Two agents (a la Gale and Hellwig, 1985):

Entrepreneurs:

  • seek loans to finance idea/project

Lenders:

  • provide funds subject to zero profits

Debt defaultable; seizing collateral requires enforcement that is capacity constrained

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SLIDE 22

Model

Drozd and Serrano-Padial: Credit Enforcement Cycles

Two agents (a la Gale and Hellwig, 1985):

Entrepreneurs:

  • seek loans to finance idea/project

Lenders:

  • provide funds subject to zero profits

Debt defaultable; seizing collateral requires enforcement that is capacity constrained Enforcement capacity accumulated ex- ante by a planner

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SLIDE 23

Timing

Drozd and Serrano-Padial: Credit Enforcement Cycles

(1) ¡ ¡ Capacity ¡ Accumula5on ¡ ¡ (2) ¡ ¡ Credit ¡ ¡ ¡ (3) ¡ Enforcement ¡ ¡ ¡

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SLIDE 24

Enforcement

Drozd and Serrano-Padial: Credit Enforcement Cycles

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SLIDE 25

Entrepreneurs

Drozd and Serrano-Padial: Credit Enforcement Cycles

Measure one of risk-neutral entrepreneurs with loan b from lender(s)

  • invest y + b and receive (y + b)w, w ∈ [0, ∞) is private info, w ∼ F

F unrestricted, but in presentation single-peaked (log-normal, Pareto)

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SLIDE 26

Entrepreneurs

Drozd and Serrano-Padial: Credit Enforcement Cycles

Measure one of risk-neutral entrepreneurs with loan b from lender(s)

  • invest y + b and receive (y + b)w, w ∈ [0, ∞) is private info, w ∼ F

F unrestricted, but in presentation single-peaked (log-normal, Pareto)

  • 2. Simultaneously decide whether to repay ¯

b ≡ ¯ w(y + b) or default

  • if default and
  • face enforcement, lose the project and get 0
  • not enforced, get a share γ of liquidation value µ(y + b)w
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SLIDE 27

Entrepreneurs

Drozd and Serrano-Padial: Credit Enforcement Cycles

Measure one of risk-neutral entrepreneurs with loan b from lender(s)

  • invest y + b and receive (y + b)w, w ∈ [0, ∞) is private info, w ∼ F

F unrestricted, but in presentation single-peaked (log-normal, Pareto)

  • 2. Simultaneously decide whether to repay ¯

b ≡ ¯ w(y + b) or default

  • if default and
  • face enforcement, lose the project and get 0
  • not enforced, get a share γ of liquidation value µ(y + b)w

Lemma Entrepreneurs default iff E(P) ≥ θ ¯

w, where θ ¯ w(w) := 1 − 1 µγ

  • 1 − ¯

w w

  • .
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SLIDE 28

Enforcement Technology

Drozd and Serrano-Padial: Credit Enforcement Cycles

Enforcement of defaulted loans is limited by capacity fixed capacity X: default rate ψ ≤ enforcement capacity (X) ⇒ P ≤ X/ψ

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SLIDE 29

Common Knowledge-Equilibrium

Drozd and Serrano-Padial: Credit Enforcement Cycles

Higher ψ lower P ⇒ Strategic complementarities ⇒ Multiple equilibria

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Common Knowledge-Equilibrium

Drozd and Serrano-Padial: Credit Enforcement Cycles

Higher ψ lower P ⇒ Strategic complementarities ⇒ Multiple equilibria let ˆ w be threshold type indifferent between defaulting or not

  • bserve default rate is ψ = F( ˆ

w) for equilibrium must have: θ( ˆ w) = P = X/F( ˆ w) → θ( ˆ w)F( ˆ w) = X

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Multiplicity under Common-Knowledge

Drozd and Serrano-Padial: Credit Enforcement Cycles

w θ (w) F(w) X ¯ X w2 w3 ¯ w X

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SLIDE 32

Not a Satisfactory Equilibrium Concept?

Drozd and Serrano-Padial: Credit Enforcement Cycles

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SLIDE 33

Not a Satisfactory Equilibrium Concept?

Drozd and Serrano-Padial: Credit Enforcement Cycles

Multiplicity relies on common knowledge of ψ (higher order beliefs)

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Not a Satisfactory Equilibrium Concept?

Drozd and Serrano-Padial: Credit Enforcement Cycles

Multiplicity relies on common knowledge of ψ (higher order beliefs) Small uncertainty regarding X can eliminate multiplicity

  • creates strategic uncertainty (ψ no longer common knowledge)
  • strategic uncertainty tampers coordination ⇒ uniqueness

GG-Eqiulibrium: agents receive a noisy signal: x = X + νη ν > 0 scale factor, η ∈ [−1/2, 1/2 ] i.i.d. with distribution H

GG intuition

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SLIDE 35

GG-Equilibrium

Drozd and Serrano-Padial: Credit Enforcement Cycles

Proposition (uniqueness) The enforcement game has a unique limit equilibrium characterized by a (weakly) decreasing threshold k(w) on signal x such that: if x ≥ k(w), agents choose to repay (a = 1) if x < k(w), agents choose to default (a = 0)

solution

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SLIDE 36

GG-Equilibrium

Drozd and Serrano-Padial: Credit Enforcement Cycles

Proposition (uniqueness) The enforcement game has a unique limit equilibrium characterized by a (weakly) decreasing threshold k(w) on signal x such that: if x ≥ k(w), agents choose to repay (a = 1) if x < k(w), agents choose to default (a = 0) Equilibrium fully characterized by indifference conditions: lim

ν→0 E[P|x = k(w)] = θ ¯ w(w)

∀w s.t. θ ¯

w(w) ∈ [0, 1]

solution

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GG-Equilibrium Strategy

Drozd and Serrano-Padial: Credit Enforcement Cycles

Proposition (equilibrium strategy) In the limit k(w) is given by: k(w) =      θ(w∗)F(w∗) for all w ∈ ( ¯ w, w∗] θ(w)F(w) for all w > w∗ where w∗ ≥ ¯ w and w∗ has two possible values: 1 If ¯ w ≥ wmax, w∗ = ¯ w 2 If ¯ w < wmax, w∗ is the unique solution to θ(w∗)F(w∗) (1 − log θ(w∗)) − F( ¯ w) = w∗

¯ w

θ(w)dF(w)

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SLIDE 38

GG-Equilibrium Strategy

Drozd and Serrano-Padial: Credit Enforcement Cycles

w k(w) w∗ ¯ w θ(w)F(w)

θ(w∗)F(w∗) (1 − log θ(w∗)) − F( ¯ w) = w∗

¯ w

θ(w)f(w)dw

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SLIDE 39

Intuition Behind Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Consider two types:

mh = 60% have θh ml = 20% have θl < θh (but close enough)

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Intuition Behind Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Consider two types:

mh = 60% have θh ml = 20% have θl < θh (but close enough)

2

What makes kl ց kh?

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SLIDE 41

Intuition Behind Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Consider two types:

mh = 60% have θh ml = 20% have θl < θh (but close enough)

2

What makes kl ց kh?

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SLIDE 42

Intuition Behind Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Consider two types:

mh = 60% have θh ml = 20% have θl < θh (but close enough)

2

What makes kl ց kh?

When h receives kh, she thinks ψ = 1

2ml = 30%

When l receives kl > kh, she thinks ψ = 1

2ml + mh/2 = 70%

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SLIDE 43

Intuition Behind Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Consider two types:

mh = 60% have θh ml = 20% have θl < θh (but close enough)

2

What makes kl ց kh?

When h receives kh, she thinks ψ = 1

2ml = 30%

When l receives kl > kh, she thinks ψ = 1

2ml + mh/2 = 70% ⇒ Pl < Ph

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SLIDE 44

Endogenous Credit

Drozd and Serrano-Padial: Credit Enforcement Cycles

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SLIDE 45

Timing

Drozd and Serrano-Padial: Credit Enforcement Cycles

(1) ¡ ¡ Capacity ¡ Accumula5on ¡ ¡ (2) ¡ ¡ Credit ¡ ¡ ¡ (3) ¡ Enforcement ¡ ¡ ¡

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SLIDE 46

Endogenous Credit Setup

Drozd and Serrano-Padial: Credit Enforcement Cycles

Lenders issue credit contracts (b, ¯ w) bertrand competition: loan maximizes agents’ payoffs s.t. zero profits.

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SLIDE 47

Endogenous Credit Setup

Drozd and Serrano-Padial: Credit Enforcement Cycles

Lenders issue credit contracts (b, ¯ w) bertrand competition: loan maximizes agents’ payoffs s.t. zero profits.

Optimization Problems

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SLIDE 48

Comparative Statics

Drozd and Serrano-Padial: Credit Enforcement Cycles

Shock tangles measure s of enforcement capacity: X′ = X − s

  • equivalent to an exogenous shift in distribution of returns
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SLIDE 49

Comparative Statics

Drozd and Serrano-Padial: Credit Enforcement Cycles

Proposition If X ≥ k(w∗) at the optimal contract then b and ¯ w increase (decrease) with X.

w k(w) ¯ w high credit ¯ w′ low credit X ˆ w X′

Heterogeneity

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SLIDE 50

Calibrated Numerical Example

Drozd and Serrano-Padial: Credit Enforcement Cycles

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SLIDE 51

Timing

Drozd and Serrano-Padial: Credit Enforcement Cycles

(1) ¡ ¡ Capacity ¡ Accumula5on ¡ ¡ (2) ¡ ¡ Credit ¡ ¡ ¡ (3) ¡ Enforcement ¡ ¡ ¡

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SLIDE 52

Endogenous Enforcement Setup

Drozd and Serrano-Padial: Credit Enforcement Cycles

Planner chooses enforcement capacity X at a cost c(X) maximizes expected agent payoffs net of capacity costs

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SLIDE 53

Calibrated Numerical Example

Drozd and Serrano-Padial: Credit Enforcement Cycles

  • 1. Calibrate to U.S. data (large shock, small shock)

Example

  • 2. Show:
  • shock that lowers X (or affects F) leads to a severe credit crunch
  • propagation even if there is ample capacity to accommodate the shock.
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SLIDE 54

Transmission of Calibrated Shocks

Drozd and Serrano-Padial: Credit Enforcement Cycles

Binary shock s reduces capacity to X = Xo − s before credit market opens (↑ default rate on existing loans ⇒ ↓ residual capacity for new loans)

0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Pr(s > 0) b b(s = 1.8%) b(s = 0) Crisis Shock

0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Pr(s > 0) b b(s = 0.4%) b(s = 0) Average Shock

Credit enforcement cycle: (potential dynamics) ↑ ψ ⇒ ↓ X ⇒ ↓ b ⇒ ↓ ψ ...

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SLIDE 55

Conclusions

Drozd and Serrano-Padial: Credit Enforcement Cycles

Framework to study endogenous enforcement

  • Focus on link between enforcement institutions and credit

fluctuations

  • Approach applicable to other default spillovers (e.g., endogenous

collateral values) Developed method to deal with equilibrium indeterminacy under heterogeneity, suitable for quantitative work Economic fragility despite substantial heterogeneity

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SLIDE 56

Drozd and Serrano-Padial: Credit Enforcement Cycles

NEW YORK (CNNMoney, 2012) – Borrowers facing foreclosure are learning that they can stay in their homes for years (...) Among the tactics: Challenging the bank’s actions, waiting to file paperwork right up until the deadline, requesting the lender dig up original paperwork or, in some extreme cases, declaring

  • bankruptcy. Nationwide, the average time it takes to process a foreclosure has

climbed to 674 days from 253 days just four years ago (...).

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SLIDE 57

Backup Slides

Drozd and Serrano-Padial: Credit Enforcement Cycles

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SLIDE 58

Related Literature

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Law and Finance: enforcement and credit

  • La Porta et al (1990), Djankov et al (2007, 2008)
  • Our paper: (endogenous) enforcement and credit volatility

2

Enforcement externalities:

  • Bond and Rai (2009), Arellano and Kotcherlakota (2009), tax evasion

and crime literature.

3

Global Games

  • Carlsson and Van Damme (1993), Morris and Shin (1998, 2003),

Frankel, Morris and Pauzner (2003), Sakovics and Steiner (2012)

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SLIDE 59

Lender and Planner Problems

Drozd and Serrano-Padial: Credit Enforcement Cycles

Lenders: (a = 1 denotes repay) V (X) := max

b, ¯ w,P

  • {w:a=1}

(y + b)(w − ¯ w)dF + (1 − P)

  • {w:a=0}

γµ(y + b)wdF

  • s.t. P ≤ min
  • X

ψ , 1

  • and

b ≤

  • {w:a=1}

(y + b) ¯ wdF + P

  • {w:a=0}

µ(y + b)wdF +(1 − P)

  • {w:a=0}

(1 − γ)µ(y + b)wdF

go back

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SLIDE 60

Intuition For Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Thresholds must be decreasing in w (lower propensity to default ⇒ lower k)

2

k(·) strictly decreasing ⇒ As ν → 0 agent believes ψ = F(w) at x = k(w)

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SLIDE 61

Intuition For Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Thresholds must be decreasing in w (lower propensity to default ⇒ lower k)

2

k(·) strictly decreasing ⇒ As ν → 0 agent believes ψ = F(w) at x = k(w)

3

k(w) ց k(w′) for w < w′ < wmax

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SLIDE 62

Intuition For Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Thresholds must be decreasing in w (lower propensity to default ⇒ lower k)

2

k(·) strictly decreasing ⇒ As ν → 0 agent believes ψ = F(w) at x = k(w)

3

k(w) ց k(w′) for w < w′ < wmax θ ↓ but ψ ↑↑ (mass concentrated to the left of wmax)

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SLIDE 63

Intuition For Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Thresholds must be decreasing in w (lower propensity to default ⇒ lower k)

2

k(·) strictly decreasing ⇒ As ν → 0 agent believes ψ = F(w) at x = k(w)

3

k(w) ց k(w′) for w < w′ < wmax θ ↓ but ψ ↑↑ (mass concentrated to the left of wmax) ⇓ E(P|x = k) ↓↓ < θ ↓

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SLIDE 64

Intuition For Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Thresholds must be decreasing in w (lower propensity to default ⇒ lower k)

2

k(·) strictly decreasing ⇒ As ν → 0 agent believes ψ = F(w) at x = k(w)

3

k(w) ց k(w′) for w < w′ < wmax θ ↓ but ψ ↑↑ (mass concentrated to the left of wmax) ⇓ E(P|x = k) ↓↓ < θ ↓ ⇓ Snowballing: agent with w′ wants to default at higher signals, k(w′) ↑

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SLIDE 65

The Impact of Heterogeneity

Drozd and Serrano-Padial: Credit Enforcement Cycles

F = Lognormal, Ew = 1.02, µ = 0.88 (Bernanke et al; 1999), y = 1, γ = 0.25

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.01 0.02 0.03 0.04 0.05 X

b/y σ = 1

16

σ = 1

8

σ = 1

4

σ = 3

8 0.01 0.02 0.03 0.04 0.05 0.01 0.02 0.03 0.04 0.05 X

ψ σ = 1

16

σ = 1

8

σ = 1

4

σ = 3

8

concentrated returns ⇒ negligible insolvency rate, cluster too large (60%)

go back

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SLIDE 66

The Impact of Heterogeneity

Drozd and Serrano-Padial: Credit Enforcement Cycles

1 2 3 4 5 6 0.5 1.0 1.5 2.0

w f(w) σ = 1

16

σ = 1

8

σ = 1

4

σ = 3

8

go back

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SLIDE 67

Optimal capacity: Borrowing constraint

Drozd and Serrano-Padial: Credit Enforcement Cycles

σ = 3/8, c(X) = 0.088X Statistic Value Target b/y 0.8 0.5 - 1 ψ 2.3% 2.3% ROE 3.4% c(Xo)/ROE 0.06 Utilization ( ψ

X )

95% Cluster 1.7% % Strategic 6.9% Borrowing constraint: b is 20% lower than without externality (γ = 0)

go back

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SLIDE 68

Uniqueness

Drozd and Serrano-Padial: Credit Enforcement Cycles

If agent receives x then X ∈ [x − ν/2, x + ν/2] and other agents’ signals are in [x − ν, x + ν] Proof sketch:

1 There is a lowest and highest equilibria, both in threshold

strategies (resp. k and k)

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SLIDE 69

Uniqueness

Drozd and Serrano-Padial: Credit Enforcement Cycles

If agent receives x then X ∈ [x − ν/2, x + ν/2] and other agents’ signals are in [x − ν, x + ν] Proof sketch:

1 There is a lowest and highest equilibria, both in threshold

strategies (resp. k and k)

2 Assume that k(w) = k(w) + ∆ for all w 3 Agent beliefs when x = k(w) under k, relative to x = k(w) under

k: X went up by ∆ on average

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SLIDE 70

Uniqueness

Drozd and Serrano-Padial: Credit Enforcement Cycles

If agent receives x then X ∈ [x − ν/2, x + ν/2] and other agents’ signals are in [x − ν, x + ν] Proof sketch:

1 There is a lowest and highest equilibria, both in threshold

strategies (resp. k and k)

2 Assume that k(w) = k(w) + ∆ for all w 3 Agent beliefs when x = k(w) under k, relative to x = k(w) under

k: X went up by ∆ on average strategic beliefs about ψ are the same! (translation invariant)

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SLIDE 71

Uniqueness

Drozd and Serrano-Padial: Credit Enforcement Cycles

If agent receives x then X ∈ [x − ν/2, x + ν/2] and other agents’ signals are in [x − ν, x + ν] Proof sketch:

1 There is a lowest and highest equilibria, both in threshold

strategies (resp. k and k)

2 Assume that k(w) = k(w) + ∆ for all w 3 Agent beliefs when x = k(w) under k, relative to x = k(w) under

k: X went up by ∆ on average strategic beliefs about ψ are the same! (translation invariant)

4 Either k or k violates indifference conditions 5 Argument generalizes to unequal ∆ ⇒ eq. uniqueness

slide-72
SLIDE 72

Drozd and Serrano-Padial: Credit Enforcement Cycles

NEW YORK (CNNMoney, 2012) – Borrowers facing foreclosure are learning that they can stay in their homes for years (...) Among the tactics: Challenging the bank’s actions, waiting to file paperwork right up until the deadline, requesting the lender dig up original paperwork or, in some extreme cases, declaring

  • bankruptcy. Nationwide, the average time it takes to process a foreclosure has

climbed to 674 days from 253 days just four years ago (...).

slide-73
SLIDE 73

Backup Slides

Drozd and Serrano-Padial: Credit Enforcement Cycles

slide-74
SLIDE 74

Enforcement Delays

Drozd and Serrano-Padial: Credit Enforcement Cycles

375 ¡ 400 ¡ 425 ¡ 450 ¡ 475 ¡ 500 ¡ 525 ¡ 550 ¡ 800,000 ¡ 900,000 ¡ 1,000,000 ¡ 1,100,000 ¡ 1,200,000 ¡ 1,300,000 ¡ 1,400,000 ¡ 1,500,000 ¡ 1,600,000 ¡ 2007 ¡ 2008 ¡ 2009 ¡ 2010 ¡ 2011 ¡ 2012 ¡ 2013 ¡ 2014 ¡ 2015 ¡ Days ¡ Cases ¡

U.S. ¡

New ¡Cases ¡ Delay ¡(days) ¡ ¡1,150 ¡ ¡ ¡1,200 ¡ ¡ ¡1,250 ¡ ¡ ¡1,300 ¡ ¡ ¡1,350 ¡ ¡ ¡1,400 ¡ ¡ ¡1,450 ¡ ¡ ¡1,500 ¡ ¡ ¡1,550 ¡ ¡ 50,000 ¡ 55,000 ¡ 60,000 ¡ 65,000 ¡ 70,000 ¡ 75,000 ¡ 80,000 ¡ 2007 ¡ 2008 ¡ 2009 ¡ 2010 ¡ 2011 ¡ 2012 ¡ 2013 ¡ 2014 ¡ 2015 ¡ Days ¡ Cases ¡

ITALY ¡

New ¡Cases ¡ Delay ¡(days) ¡ 500 ¡ 700 ¡ 900 ¡ 1100 ¡ 1300 ¡ 1500 ¡ 1700 ¡ 1900 ¡ 1,000 ¡ 3,000 ¡ 5,000 ¡ 7,000 ¡ 9,000 ¡ 11,000 ¡ 2007 ¡ 2008 ¡ 2009 ¡ 2010 ¡ 2011 ¡ 2012 ¡ 2013 ¡ 2014 ¡ 2015 ¡ Days ¡ Cases ¡

SPAIN ¡

New ¡Cases ¡ Delay ¡(days) ¡

Figure : Default Cases (left axis) and Enforcement Delay (right axis)

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SLIDE 75

How We Solve the Game

Drozd and Serrano-Padial: Credit Enforcement Cycles

For limν→0 k(w) equilibrium satisfies: E[P|x = k(w)] = θ(w) ∀w s.t. θ(w) ∈ (0, 1) Beliefs about X approximate true X as ν → 0 How about strategic beliefs about ψ?

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SLIDE 76

How We Solve the Game

Drozd and Serrano-Padial: Credit Enforcement Cycles

For limν→0 k(w) equilibrium satisfies: E[P|x = k(w)] = θ(w) ∀w s.t. θ(w) ∈ (0, 1) Beliefs about X approximate true X as ν → 0 How about strategic beliefs about ψ? Laplacian Property: if k(w) = k for all w ⇒ ψ|x = k uniformly distributed Under heterogeneous k(w) the Laplacian property holds ‘on average’ (Sakovics-Steiner, 2012 )

Cluster of thresholds converging to the same limit ⇒ average the indifference conditions and replace the average belief by the uniform distribution Use monotonicity of θ to identify the cluster bounds

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SLIDE 77

The Belief Constraint (Sakovics-Steiner, 2012)

Drozd and Serrano-Padial: Credit Enforcement Cycles

Equilibrium fully characterized by indifference conditions: lim

ν→0 E[P|x = k(w)] = θ ¯ w(w)

∀w s.t. θ ¯

w(w) ∈ [0, 1]

Lemma (belief-constraint) Let ψ(W ′) be the default rate in some measurable set W ′ ⊆ [0, ∞). Then, for any z ∈ [0, 1], 1

  • W ′ f(w)dw
  • W ′ Pw
  • ψ(W ′) ≤ z
  • x = k(w)
  • f(w)dw = z,

where Pw

  • ·
  • x = k(w)
  • is the probability assessment of the default rate in W ′ by

an agent whose signal x is equal to her threshold k(w).

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SLIDE 78

The Belief Constraint

Drozd and Serrano-Padial: Credit Enforcement Cycles

𝑌 ¡ 𝑦 ¡ Xz(w) ¡ Xz(w’) ¡ k(w) ¡ k(w’) ¡

Belief asymmetry between w and w′ regarding each other actions in [k(w), k(w′)] averages out

go back

slide-79
SLIDE 79

Basic Idea

Drozd and Serrano-Padial: Credit Enforcement Cycles

𝑦 ¡

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SLIDE 80

Basic Idea

Drozd and Serrano-Padial: Credit Enforcement Cycles

𝑦 ¡ 𝑦 ¡

go back

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SLIDE 81

Identification

Drozd and Serrano-Padial: Credit Enforcement Cycles

F = Lognormal, Ew = 1.02, µ = 0.88 (Bernanke et al; 1999), y = 1, γ = 0.25

Return Distributions

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.01 0.02 0.03 0.04 0.05 X

b/y σ = 1

16

σ = 1

8

σ = 1

4

σ = 3

8 0.01 0.02 0.03 0.04 0.05 0.01 0.02 0.03 0.04 0.05 X

ψ σ = 1

16

σ = 1

8

σ = 1

4

σ = 3

8

concentrated returns ⇒ negligible insolvency rate, cluster too large (60%)

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SLIDE 82

Extended Intuition For Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Thresholds must be decreasing in w (lower propensity to default ⇒ lower k)

2

k(·) strictly decreasing ⇒ As ν → 0 agent believes ψ = F(w) at x = k(w)

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SLIDE 83

Extended Intuition For Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Thresholds must be decreasing in w (lower propensity to default ⇒ lower k)

2

k(·) strictly decreasing ⇒ As ν → 0 agent believes ψ = F(w) at x = k(w)

3

k(w) ց k(w′) for w < w′ < wmax

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SLIDE 84

Extended Intuition For Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Thresholds must be decreasing in w (lower propensity to default ⇒ lower k)

2

k(·) strictly decreasing ⇒ As ν → 0 agent believes ψ = F(w) at x = k(w)

3

k(w) ց k(w′) for w < w′ < wmax θ ↓ but ψ ↑↑ (mass concentrated to the left of wmax)

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SLIDE 85

Extended Intuition For Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Thresholds must be decreasing in w (lower propensity to default ⇒ lower k)

2

k(·) strictly decreasing ⇒ As ν → 0 agent believes ψ = F(w) at x = k(w)

3

k(w) ց k(w′) for w < w′ < wmax θ ↓ but ψ ↑↑ (mass concentrated to the left of wmax) ⇓ E(P|x = k) ↓↓ < θ ↓

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SLIDE 86

Extended Intuition For Clustering

Drozd and Serrano-Padial: Credit Enforcement Cycles 1

Thresholds must be decreasing in w (lower propensity to default ⇒ lower k)

2

k(·) strictly decreasing ⇒ As ν → 0 agent believes ψ = F(w) at x = k(w)

3

k(w) ց k(w′) for w < w′ < wmax θ ↓ but ψ ↑↑ (mass concentrated to the left of wmax) ⇓ E(P|x = k) ↓↓ < θ ↓ ⇓ Snowballing: agent with w′ wants to default at higher signals, k(w′) ↑

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SLIDE 87

Sketch of Proof of Uniqueness

Drozd and Serrano-Padial: Credit Enforcement Cycles

If agent receives x then X ∈ [x − ν/2, x + ν/2] and other agents’ signals are in [x − ν, x + ν] Proof sketch:

1 There is a lowest and highest equilibria, both in threshold

strategies (resp. k and k)

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SLIDE 88

Sketch of Proof of Uniqueness

Drozd and Serrano-Padial: Credit Enforcement Cycles

If agent receives x then X ∈ [x − ν/2, x + ν/2] and other agents’ signals are in [x − ν, x + ν] Proof sketch:

1 There is a lowest and highest equilibria, both in threshold

strategies (resp. k and k)

2 Assume that k(w) = k(w) + ∆ for all w 3 Agent beliefs when x = k(w) under k, relative to x = k(w) under

k: X went up by ∆ on average

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SLIDE 89

Sketch of Proof of Uniqueness

Drozd and Serrano-Padial: Credit Enforcement Cycles

If agent receives x then X ∈ [x − ν/2, x + ν/2] and other agents’ signals are in [x − ν, x + ν] Proof sketch:

1 There is a lowest and highest equilibria, both in threshold

strategies (resp. k and k)

2 Assume that k(w) = k(w) + ∆ for all w 3 Agent beliefs when x = k(w) under k, relative to x = k(w) under

k: X went up by ∆ on average strategic beliefs about ψ are the same! (translation invariant)

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SLIDE 90

Sketch of Proof of Uniqueness

Drozd and Serrano-Padial: Credit Enforcement Cycles

If agent receives x then X ∈ [x − ν/2, x + ν/2] and other agents’ signals are in [x − ν, x + ν] Proof sketch:

1 There is a lowest and highest equilibria, both in threshold

strategies (resp. k and k)

2 Assume that k(w) = k(w) + ∆ for all w 3 Agent beliefs when x = k(w) under k, relative to x = k(w) under

k: X went up by ∆ on average strategic beliefs about ψ are the same! (translation invariant)

4 Either k or k violates indifference conditions 5 Argument generalizes to unequal ∆ ⇒ eq. uniqueness