Bank Competition, Information Choice andInefficient Lending Booms

Silvio Petriconi

Bocconi University and IGIERsilvio.petriconi@unibocconi.it

Jun 24, 2014

Introduction

Motivation

I in the last two decades we have seen substantial deregulation ofbanking industry in most countries (Abiad et al., 2008)

I in the U.S.,I 1994 Riegle-Neal Act: no more interstate banking and branching

restrictionsI 1999 Gramm-Leach-Bliley Act: lifting of Glass-Steagall separation

between investment banking and commercial banking

I these reforms have increased banking competition and are thoughtto have increased availability of credit

I but is it possible that competition has prompted too much lending?I U.S. Senior Loan Officer Survey hints at a competition channel

behind the 2003-2006 boom in residential mortgage lending

Can more banking competition foster inefficient lending booms?

2

Introduction

Motivation

I in the last two decades we have seen substantial deregulation ofbanking industry in most countries (Abiad et al., 2008)

I in the U.S.,I 1994 Riegle-Neal Act: no more interstate banking and branching

restrictionsI 1999 Gramm-Leach-Bliley Act: lifting of Glass-Steagall separation

between investment banking and commercial banking

I these reforms have increased banking competition and are thoughtto have increased availability of credit

I but is it possible that competition has prompted too much lending?I U.S. Senior Loan Officer Survey hints at a competition channel

behind the 2003-2006 boom in residential mortgage lending

Can more banking competition foster inefficient lending booms?

2

Introduction

Motivation

I in the last two decades we have seen substantial deregulation ofbanking industry in most countries (Abiad et al., 2008)

I in the U.S.,I 1994 Riegle-Neal Act: no more interstate banking and branching

restrictionsI 1999 Gramm-Leach-Bliley Act: lifting of Glass-Steagall separation

between investment banking and commercial banking

I these reforms have increased banking competition and are thoughtto have increased availability of credit

I but is it possible that competition has prompted too much lending?I U.S. Senior Loan Officer Survey hints at a competition channel

behind the 2003-2006 boom in residential mortgage lending

Can more banking competition foster inefficient lending booms?

2

Introduction

Motivation

I in the last two decades we have seen substantial deregulation ofbanking industry in most countries (Abiad et al., 2008)

I in the U.S.,I 1994 Riegle-Neal Act: no more interstate banking and branching

restrictionsI 1999 Gramm-Leach-Bliley Act: lifting of Glass-Steagall separation

between investment banking and commercial banking

I these reforms have increased banking competition and are thoughtto have increased availability of credit

I but is it possible that competition has prompted too much lending?I U.S. Senior Loan Officer Survey hints at a competition channel

behind the 2003-2006 boom in residential mortgage lending

Can more banking competition foster inefficient lending booms?

2

Key Results

Today I show you a model in which increasing bank competition exertsharmful pressure on lending standards.

I have two key results:

1. competition inefficiently lowers lending standards and increases thenumber of bad loans

2. more competition reduces lenders’ incentives to screen theirborrowers thoroughly

Both effects are procyclical.

Together, they match the stylized facts about lending booms quite well.

3

Key Results

Today I show you a model in which increasing bank competition exertsharmful pressure on lending standards.

I have two key results:

1. competition inefficiently lowers lending standards and increases thenumber of bad loans

2. more competition reduces lenders’ incentives to screen theirborrowers thoroughly

Both effects are procyclical.

Together, they match the stylized facts about lending booms quite well.

3

Key Results

Today I show you a model in which increasing bank competition exertsharmful pressure on lending standards.

I have two key results:

1. competition inefficiently lowers lending standards and increases thenumber of bad loans

2. more competition reduces lenders’ incentives to screen theirborrowers thoroughly

Both effects are procyclical.

Together, they match the stylized facts about lending booms quite well.

3

Key Results

Today I show you a model in which increasing bank competition exertsharmful pressure on lending standards.

I have two key results:

1. competition inefficiently lowers lending standards and increases thenumber of bad loans

2. more competition reduces lenders’ incentives to screen theirborrowers thoroughly

Both effects are procyclical.

Together, they match the stylized facts about lending booms quite well.

3

Intuition

Informational SpilloversAssume for example the following legislation:

I banks have to make credit offers in writing

I no fees for loan applications

Then informed banks’ actions become observable to uninformedcompetitors −→ informational free-riding!

The informed bank’s optimal response to threat of entry byinformational free-riders:

I “poison the well” by making bad loans to prevent customer poaching

I approval of bad loans implies poor use of information from screening=⇒ choose less precise screening ex-ante

With more competition, these distortions become more pronounced.

4

Intuition

Informational SpilloversAssume for example the following legislation:

I banks have to make credit offers in writing

I no fees for loan applications

Then informed banks’ actions become observable to uninformedcompetitors −→ informational free-riding!

The informed bank’s optimal response to threat of entry byinformational free-riders:

I “poison the well” by making bad loans to prevent customer poaching

I approval of bad loans implies poor use of information from screening=⇒ choose less precise screening ex-ante

With more competition, these distortions become more pronounced.

4

Intuition

Informational SpilloversAssume for example the following legislation:

I banks have to make credit offers in writing

I no fees for loan applications

Then informed banks’ actions become observable to uninformedcompetitors −→ informational free-riding!

The informed bank’s optimal response to threat of entry byinformational free-riders:

I “poison the well” by making bad loans to prevent customer poaching

I approval of bad loans implies poor use of information from screening=⇒ choose less precise screening ex-ante

With more competition, these distortions become more pronounced.

4

Intuition

Informational SpilloversAssume for example the following legislation:

I banks have to make credit offers in writing

I no fees for loan applications

Then informed banks’ actions become observable to uninformedcompetitors −→ informational free-riding!

The informed bank’s optimal response to threat of entry byinformational free-riders:

I “poison the well” by making bad loans to prevent customer poaching

I approval of bad loans implies poor use of information from screening=⇒ choose less precise screening ex-ante

With more competition, these distortions become more pronounced.

4

Related Literature

Literature on Competition and Credit Screening

I Broecker (1990), Riordan (1993), Gehrig (1998), Ruckes (2004),Ogura (2006), Direr (2008)

Adverse Selection to Deter Entry

I Dell’Ariccia et al. (1999)

Competition in Banking and Information Choice

I Hauswald and Marquez (2003), Hauswald and Marquez (2006)

Theories of Lending Booms

I Rajan (1994), Dell’Ariccia and Marquez (2006),Lorenzoni (2008)

Empirical Literature on Lending Procyclicality and Booms

I Gourinchas et al. (2001), Borio and Lowe (2002),Bordo and Jeanne (2002)

I Berger and Udell (2005), Lown and Morgan (2006)

5

Outline

Outline:

The Model

Planner’s Solution

Two Key Results about Equilibrium under Competition

Lending Cycles

Conclusions

6

The Model

7

Model (I)

Heterogeneous Entrepreneurs:

I two islands j ∈ {1, 2}I each island has a continuum of mass 1 of wealthless entrepreneurs,

indexed by i ∈ [0, 1]

I option to run risky project: invest one unit at time t, obtain in t + 1a payoff

Xi =

R with probability pi

r with probability 1− pi

(1)

I pi ∼ U(p̄ − ε2 , p̄ + ε

2 ), private knowledge

I no signaling or self-selection mechanisms available

8

Model (II)

Bank:

I one risk neutral bank on each island with unlimited access to fundsat cost ρ

I can lend both domestically and on other islands

I lending abroad incurs extra cost γ > 0 per loan

I bank uses costless credit-worthiness test to assess borrower quality

I precision of the test is given by the bank’s screening precisionλ ∈ [0, 1)

I screening precision λ is costly: convex cost function c(λ) withc(0) = 0, c ′(λ) > 0, lim

λ→1c(λ) =∞.

I screening works only for entrepreneurs on the same island

9

Model (II)

Bank:

I one risk neutral bank on each island with unlimited access to fundsat cost ρ

I can lend both domestically and on other islands

I lending abroad incurs extra cost γ > 0 per loan

I bank uses costless credit-worthiness test to assess borrower quality

I precision of the test is given by the bank’s screening precisionλ ∈ [0, 1)

I screening precision λ is costly: convex cost function c(λ) withc(0) = 0, c ′(λ) > 0, lim

λ→1c(λ) =∞.

I screening works only for entrepreneurs on the same island

9

Model (II)

Bank:

I one risk neutral bank on each island with unlimited access to fundsat cost ρ

I can lend both domestically and on other islands

I lending abroad incurs extra cost γ > 0 per loan

I bank uses costless credit-worthiness test to assess borrower quality

I precision of the test is given by the bank’s screening precisionλ ∈ [0, 1)

I screening precision λ is costly: convex cost function c(λ) withc(0) = 0, c ′(λ) > 0, lim

λ→1c(λ) =∞.

I screening works only for entrepreneurs on the same island

9

Model (II)

Bank:

I one risk neutral bank on each island with unlimited access to fundsat cost ρ

I can lend both domestically and on other islands

I lending abroad incurs extra cost γ > 0 per loan

I bank uses costless credit-worthiness test to assess borrower quality

I precision of the test is given by the bank’s screening precisionλ ∈ [0, 1)

I screening precision λ is costly: convex cost function c(λ) withc(0) = 0, c ′(λ) > 0, lim

λ→1c(λ) =∞.

I screening works only for entrepreneurs on the same island

9

Model (II)

Bank:

I one risk neutral bank on each island with unlimited access to fundsat cost ρ

I can lend both domestically and on other islands

I lending abroad incurs extra cost γ > 0 per loan

I bank uses costless credit-worthiness test to assess borrower quality

I precision of the test is given by the bank’s screening precisionλ ∈ [0, 1):

I test yields the true type pi with probability λ, otherwise randomnoise that is drawn from prior distribution

I the bank does not know whether signal is informative or just noise,uses Bayesian updating of beliefs

I screening precision λ is costly: convex cost function c(λ) withc(0) = 0, c ′(λ) > 0, lim

λ→1c(λ) =∞.

I screening works only for entrepreneurs on the same island

9

Model (II)

Bank:

I one risk neutral bank on each island with unlimited access to fundsat cost ρ

I can lend both domestically and on other islands

I lending abroad incurs extra cost γ > 0 per loan

I bank uses costless credit-worthiness test to assess borrower quality

I precision of the test is given by the bank’s screening precisionλ ∈ [0, 1)

I screening precision λ is costly: convex cost function c(λ) withc(0) = 0, c ′(λ) > 0, lim

λ→1c(λ) =∞.

I screening works only for entrepreneurs on the same island

9

Model (II)

Bank:

I one risk neutral bank on each island with unlimited access to fundsat cost ρ

I can lend both domestically and on other islands

I lending abroad incurs extra cost γ > 0 per loan

I bank uses costless credit-worthiness test to assess borrower quality

I precision of the test is given by the bank’s screening precisionλ ∈ [0, 1)

I screening precision λ is costly: convex cost function c(λ) withc(0) = 0, c ′(λ) > 0, lim

λ→1c(λ) =∞.

I screening works only for entrepreneurs on the same island

9

Model: Timing

Timing:

1. Each bankI chooses its screening precision λj (observable to everyone),I pays screening cost c(λj) andI observes private signal σi,λ for every project i ∈ [0, 1]

2. both banks choose their domestic loan portfolio comprising ofI a set Pj of projects to be offered a loan, andI state-contingent repayment terms (Di , di ) for every project i ∈ Pj .

3. each bank observes the domestic loan offers made on the otherisland and chooses whether and under which terms (O j′

i , oj′

i ) to offeroutside credit to loan-approved entrepreneurs⇒ informational spillover

4. entrepreneurs choose loan offer with lowest expected repaymentrate; if indifferent, they stay with the domestic bank.

10

Benchmark: The Planner’s Solution

11

Planner’s Solution

Planner’s Problem:

1. choose screening precision λ, pay c(λ)

2. observe signals, update beliefs, and

3. determine projects to be financed such that surplus is maximized.

Solution: by backward induction.

1. given posterior beliefs after observing the signal, findwelfare-maximizing portfolio of projects to finance

2. choose screening precision λ∗ as to maximize total welfare

12

Dispersion of Posterior Beliefs

Posterior beliefs:Bayesian updating of beliefs conditional on observing a signal realizationsi yields

E [pi |σi = si ] = λsi + (1− λ)p̄

More screening precision generates more dispersion in posteriorexpectations (see Ganuza and Penalva, 2010):

E [pi ]

p̄

prior posterior

p̄ − ε2

p̄ + ε2

13

Dispersion of Posterior Beliefs

Posterior beliefs:Bayesian updating of beliefs conditional on observing a signal realizationsi yields

E [pi |σi = si ] = λsi + (1− λ)p̄

More screening precision generates more dispersion in posteriorexpectations (see Ganuza and Penalva, 2010):

E [pi ]

p̄

prior posterior

p̄ − ε2

p̄ + ε2

13

Planner’s Optimal Portfolio Choice

Finding the marginal project:

π(q) = qR + (1− q)r − ρ != 0

⇔ q =ρ− r

R − r

Reminder:R payoff upon project successr payoff upon project failure (liquidation)ρ Bank refinancing rate

q is high in recession, low in boom.

RemarkThe planner’s optimal portfolio choice is to finance all projects for which

E [pi |si ] > q

14

Planner’s Optimal Portfolio Choice (II)Credit Mass: Size of the second-best portfolio is

mSBλ =

0 if q − p̄ ≥ +λε

2

12 −

q−p̄λε if −λε2 < q − p̄ < +λε

2

1 if q − p̄ ≤ −λε2

E [pi ]

p̄

prior posterior

p̄ − ε2

p̄ + ε2

q

15

Planner’s Optimal Portfolio Choice (II)Credit Mass: Size of the second-best portfolio is

mSBλ =

0 if q − p̄ ≥ +λε

212 −

q−p̄λε if −λε2 < q − p̄ < +λε

2

1 if q − p̄ ≤ −λε2

E [pi ]

p̄

prior posterior

p̄ − ε2

p̄ + ε2

q

15

Planner’s Optimal Portfolio Choice (II)Credit Mass: Size of the second-best portfolio is

mSBλ =

0 if q − p̄ ≥ +λε

212 −

q−p̄λε if −λε2 < q − p̄ < +λε

2

1 if q − p̄ ≤ −λε2

E [pi ]

p̄

prior posterior

p̄ − ε2

p̄ + ε2

q

15

Planner’s Optimal Portfolio Choice (II)Credit Mass: Size of the second-best portfolio is

mSBλ =

0 if q − p̄ ≥ +λε

212 −

q−p̄λε if −λε2 < q − p̄ < +λε

2

1 if q − p̄ ≤ −λε2

E [pi ]

p̄

prior posterior

p̄ − ε2

p̄ + ε2

q

15

Planner’s Optimal Portfolio Choice (II)Credit Mass: Size of the second-best portfolio is

mSBλ =

0 if q − p̄ ≥ +λε

212 −

q−p̄λε if −λε2 < q − p̄ < +λε

2

1 if q − p̄ ≤ −λε2

Which expression holds for given screening precision λ and cut-off q?

q

λ

0 1

1

p̄

15

Planner’s Optimal Portfolio Choice (II)Credit Mass: Size of the second-best portfolio is

mSBλ =

0 if q − p̄ ≥ +λε

212 −

q−p̄λε if −λε2 < q − p̄ < +λε

2

1 if q − p̄ ≤ −λε2

Which expression holds for given screening precision λ and cut-off q?

q

λ

0 1

1

p̄

15

Planner’s Optimal Portfolio Choice (II)Credit Mass: Size of the second-best portfolio is

mSBλ =

0 if q − p̄ ≥ +λε

212 −

q−p̄λε if −λε2 < q − p̄ < +λε

2

1 if q − p̄ ≤ −λε2

Which expression holds for given screening precision λ and cut-off q?

q

λ

0 1

1

p̄

1

15

Planner’s Optimal Portfolio Choice (II)Credit Mass: Size of the second-best portfolio is

mSBλ =

0 if q − p̄ ≥ +λε

212 −

q−p̄λε if −λε2 < q − p̄ < +λε

2

1 if q − p̄ ≤ −λε2

Which expression holds for given screening precision λ and cut-off q?

q

λ

0 1

1

p̄

1

2

15

Planner’s Optimal Portfolio Choice (II)Credit Mass: Size of the second-best portfolio is

mSBλ =

0 if q − p̄ ≥ +λε

212 −

q−p̄λε if −λε2 < q − p̄ < +λε

2

1 if q − p̄ ≤ −λε2

Which expression holds for given screening precision λ and cut-off q?

q

λ

0 1

1

p̄

1

2

3

15

The Planner’s Information Choice (I)Optimal choice of screening precision:

maxλ

ΠSBλ − c(λ)

s.t. λ ≥ 0

Which cost function? Use c(λ) = c0λ

1−λ which gives closed-form

solutions. Show

Optimal screening precision λ∗SB(q) as function of economic state q:

q

λ

0 1

1

p̄

16

The Planner’s Information Choice (I)Optimal choice of screening precision:

maxλ

ΠSBλ − c(λ)

s.t. λ ≥ 0

Which cost function? Use c(λ) = c0λ

1−λ which gives closed-form

solutions. Show

Optimal screening precision λ∗SB(q) as function of economic state q:

q

λ

0 1

1

p̄

16

Equilibrium under Competition:

Two Results

17

Solving for Equilibrium under Competition

Again, I solve the problem by backward induction:

1. for given screening precision λ, I find the optimal portfolio as afunction of competition.

2. I find the profit-maximizing screening precision λ∗E

18

Solving for Equilibrium under Competition

Again, I solve the problem by backward induction:

1. for given screening precision λ, I find the optimal portfolio as afunction of competition.

2. I find the profit-maximizing screening precision λ∗E

18

Equilibrium (I): γ ≥ (R−r)ε2

Monopolist’s Problem

I for γ ≥ (R−r)ε2 , each bank is always a monopolist on its island

I due to fixed project size, monopolist can extract entire projectsurplus (R, r)

I thus, maximization problem coincides with the planner’s problem

I monopolistic allocation is constrained Pareto optimal in this model!

I caution: with endogenous project size this would not be true

19

Equilibrium (II): γ < (R−r)ε2

Competition

I if γ < (R−r)ε2 , for some values of (q, λ) competition will matter.

I when is the incumbent safe from entry of competitors?

DefinitionLet P be a loan portfolio, and denote the volume of loans in the portfolioas |P|. Then, P is noncontestable if its gross surplus per loan is atmost γ: Π[P] ≤ γ|P|

I if portfolio is noncontestable and all repayment terms are equal,there is no threat of entry

I for which (q, λ) combinations is the monopolistic portfoliononcontestable?

20

Equilibrium (II): γ < (R−r)ε2

Competition

I if γ < (R−r)ε2 , for some values of (q, λ) competition will matter.

I when is the incumbent safe from entry of competitors?

DefinitionLet P be a loan portfolio, and denote the volume of loans in the portfolioas |P|. Then, P is noncontestable if its gross surplus per loan is atmost γ: Π[P] ≤ γ|P|

I if portfolio is noncontestable and all repayment terms are equal,there is no threat of entry

I for which (q, λ) combinations is the monopolistic portfoliononcontestable?

20

Noncontestability: IntuitionGraphical Representation:

I let’s draw the set of all (q, λ) for which the monopolistic portfolio is

noncontestable:{

(q, λ) ∈ [0, 1]× [0, 1] :ΠMλ (q)

mMλ (q)≤ γ

}

q

λ

0 1

1

p̄

I what happens under threat of entry, i.e. if the monopolistic portfoliois contestable?

21

Noncontestability: IntuitionGraphical Representation:

I let’s draw the set of all (q, λ) for which the monopolistic portfolio is

noncontestable:{

(q, λ) ∈ [0, 1]× [0, 1] :ΠMλ (q)

mMλ (q)≤ γ

}

p̄ − γR−r

q

λ

0 1

1

p̄

I what happens under threat of entry, i.e. if the monopolistic portfoliois contestable?

21

Noncontestability: IntuitionGraphical Representation:

I let’s draw the set of all (q, λ) for which the monopolistic portfolio is

noncontestable:{

(q, λ) ∈ [0, 1]× [0, 1] :ΠMλ (q)

mMλ (q)≤ γ

}

p̄ − γR−r

q

λ

0 1

1

p̄

I what happens under threat of entry, i.e. if the monopolistic portfoliois contestable?

21

Noncontestability: IntuitionGraphical Representation:

I let’s draw the set of all (q, λ) for which the monopolistic portfolio is

noncontestable:{

(q, λ) ∈ [0, 1]× [0, 1] :ΠMλ (q)

mMλ (q)≤ γ

}

p̄ − γR−r

q

λ

0 1

1

p̄

I what happens under threat of entry, i.e. if the monopolistic portfoliois contestable?

21

Noncontestability: IntuitionGraphical Representation:

I let’s draw the set of all (q, λ) for which the monopolistic portfolio is

noncontestable:{

(q, λ) ∈ [0, 1]× [0, 1] :ΠMλ (q)

mMλ (q)≤ γ

}

p̄ − γR−r

q

λ

0 1

1

p̄

I what happens under threat of entry, i.e. if the monopolistic portfoliois contestable?

21

Noncontestability: IntuitionGraphical Representation:

I let’s draw the set of all (q, λ) for which the monopolistic portfolio is

noncontestable:{

(q, λ) ∈ [0, 1]× [0, 1] :ΠMλ (q)

mMλ (q)≤ γ

}

p̄ − γR−r

q

λ

0 1

1

p̄

I what happens under threat of entry, i.e. if the monopolistic portfoliois contestable?

21

Noncontestability: IntuitionGraphical Representation:

I let’s draw the set of all (q, λ) for which the monopolistic portfolio is

noncontestable:{

(q, λ) ∈ [0, 1]× [0, 1] :ΠMλ (q)

mMλ (q)≤ γ

}

q

λ

0 1

1

p̄

I what happens under threat of entry, i.e. if the monopolistic portfoliois contestable?

21

Noncontestability: IntuitionGraphical Representation:

I let’s draw the set of all (q, λ) for which the monopolistic portfolio is

noncontestable:{

(q, λ) ∈ [0, 1]× [0, 1] :ΠMλ (q)

mMλ (q)≤ γ

}

p̄ − γR−r

q

λ

0 1

1

p̄

I what happens under threat of entry, i.e. if the monopolistic portfoliois contestable?

21

Noncontestability: IntuitionGraphical Representation:

I let’s draw the set of all (q, λ) for which the monopolistic portfolio is

noncontestable:{

(q, λ) ∈ [0, 1]× [0, 1] :ΠMλ (q)

mMλ (q)≤ γ

}

p̄ − γR−r

q

λ

0 1

1

p̄

I what happens under threat of entry, i.e. if the monopolistic portfoliois contestable?

21

Noncontestability: IntuitionGraphical Representation:

I let’s draw the set of all (q, λ) for which the monopolistic portfolio is

noncontestable:{

(q, λ) ∈ [0, 1]× [0, 1] :ΠMλ (q)

mMλ (q)≤ γ

}

p̄ − γR−r

q

λ

0 1

1

p̄

I what happens under threat of entry, i.e. if the monopolistic portfoliois contestable?

21

Threat of Entry

What if the incumbent chooses some contestable portfolio?

I the outside lender can profitably undercut

I it poaches all loan-approved customers

I incumbent earns zero

⇒ incumbent’s equilibrium portfolio will always be noncontestable

Two ways to make a portfolio noncontestable:

1. reduce repayment rates

2. change composition

22

Threat of Entry

What if the incumbent chooses some contestable portfolio?

I the outside lender can profitably undercut

I it poaches all loan-approved customers

I incumbent earns zero

⇒ incumbent’s equilibrium portfolio will always be noncontestable

Two ways to make a portfolio noncontestable:

1. reduce repayment rates

2. change composition

22

Threat of Entry

What if the incumbent chooses some contestable portfolio?

I the outside lender can profitably undercut

I it poaches all loan-approved customers

I incumbent earns zero

⇒ incumbent’s equilibrium portfolio will always be noncontestable

Two ways to make a portfolio noncontestable:

1. reduce repayment rates

2. change composition

22

Threat of Entry

What if the incumbent chooses some contestable portfolio?

I the outside lender can profitably undercut

I it poaches all loan-approved customers

I incumbent earns zero

⇒ incumbent’s equilibrium portfolio will always be noncontestable

Two ways to make a portfolio noncontestable:

1. reduce repayment rates

2. change composition

22

Threat of Entry

What if the incumbent chooses some contestable portfolio?

I the outside lender can profitably undercut

I it poaches all loan-approved customers

I incumbent earns zero

⇒ incumbent’s equilibrium portfolio will always be noncontestable

Two ways to make a portfolio noncontestable:

1. reduce repayment rates

2. change composition

22

Making a portfolio noncontestable

Assume P is a contestable portfolio of size m: Π[P] > γm.How can we make it noncontestable?

Via prices (repayment rates):

I construct portfolio P ′ with same projects but reduced repayments

I reduce repayments such that Π[P ′] = γm.

Via compositional changes:

I do not lower repayments but add more projects to portfolio P̃I since they have negative NPV, average profit per project falls

I for some credit mass m̃ > m, profit will be exactly Π[P̃] = γm̃

Note m̃γ > mγ⇒ second strategy is more profitable

23

Making a portfolio noncontestable

Assume P is a contestable portfolio of size m: Π[P] > γm.How can we make it noncontestable?

Via prices (repayment rates):

I construct portfolio P ′ with same projects but reduced repayments

I reduce repayments such that Π[P ′] = γm.

Via compositional changes:

I do not lower repayments but add more projects to portfolio P̃I since they have negative NPV, average profit per project falls

I for some credit mass m̃ > m, profit will be exactly Π[P̃] = γm̃

Note m̃γ > mγ⇒ second strategy is more profitable

23

Making a portfolio noncontestable

Assume P is a contestable portfolio of size m: Π[P] > γm.How can we make it noncontestable?

Via prices (repayment rates):

I construct portfolio P ′ with same projects but reduced repayments

I reduce repayments such that Π[P ′] = γm.

Via compositional changes:

I do not lower repayments but add more projects to portfolio P̃I since they have negative NPV, average profit per project falls

I for some credit mass m̃ > m, profit will be exactly Π[P̃] = γm̃

Note m̃γ > mγ⇒ second strategy is more profitable

23

Making a portfolio noncontestable

Assume P is a contestable portfolio of size m: Π[P] > γm.How can we make it noncontestable?

Via prices (repayment rates):

I construct portfolio P ′ with same projects but reduced repayments

I reduce repayments such that Π[P ′] = γm.

Via compositional changes:

I do not lower repayments but add more projects to portfolio P̃

I since they have negative NPV, average profit per project falls

I for some credit mass m̃ > m, profit will be exactly Π[P̃] = γm̃

Note m̃γ > mγ⇒ second strategy is more profitable

23

Making a portfolio noncontestable

Assume P is a contestable portfolio of size m: Π[P] > γm.How can we make it noncontestable?

Via prices (repayment rates):

I construct portfolio P ′ with same projects but reduced repayments

I reduce repayments such that Π[P ′] = γm.

Via compositional changes:

I do not lower repayments but add more projects to portfolio P̃I since they have negative NPV, average profit per project falls

I for some credit mass m̃ > m, profit will be exactly Π[P̃] = γm̃

Note m̃γ > mγ⇒ second strategy is more profitable

23

Making a portfolio noncontestable

Assume P is a contestable portfolio of size m: Π[P] > γm.How can we make it noncontestable?

Via prices (repayment rates):

I construct portfolio P ′ with same projects but reduced repayments

I reduce repayments such that Π[P ′] = γm.

Via compositional changes:

I do not lower repayments but add more projects to portfolio P̃I since they have negative NPV, average profit per project falls

I for some credit mass m̃ > m, profit will be exactly Π[P̃] = γm̃

Note m̃γ > mγ⇒ second strategy is more profitable

23

Making a portfolio noncontestable

Assume P is a contestable portfolio of size m: Π[P] > γm.How can we make it noncontestable?

Via prices (repayment rates):

I construct portfolio P ′ with same projects but reduced repayments

I reduce repayments such that Π[P ′] = γm.

Via compositional changes:

I do not lower repayments but add more projects to portfolio P̃I since they have negative NPV, average profit per project falls

I for some credit mass m̃ > m, profit will be exactly Π[P̃] = γm̃

Note m̃γ > mγ⇒ second strategy is more profitable

23

Equilibrium under Competition

When is a noncontestable portfolio an equilibrium of the game?

In the paper I show:

Any portfolio Q∗ that maximizes surplus subject to noncontestability,

maxQ=(S, (D,d))

Π[Q]

s.t. Π[Q] ≤ γ|Q|

and has the same repayment terms (D, d) for all entrepreneurs is anequilibrium.

Proof

24

Equilibrium under Competition (II)

The equilibrium has three cases:

1. competition does not matter⇒ monopolistic allocation, repayment terms (R, r).

2. there is threat of entry, but by adding some negative NPV projectsnoncontestability can be restored⇒ cross-subsidized excessive lending, repayment terms (R, r).

3. there is threat of entry, and even by financing all projects at terms(R, r) the incumbent does not regain noncontestability⇒ finance everyone, and reduce repayment terms such that Π = γ.

25

Equilibrium under Competition (II)

The equilibrium has three cases:

1. competition does not matter⇒ monopolistic allocation, repayment terms (R, r).

2. there is threat of entry, but by adding some negative NPV projectsnoncontestability can be restored⇒ cross-subsidized excessive lending, repayment terms (R, r).

3. there is threat of entry, and even by financing all projects at terms(R, r) the incumbent does not regain noncontestability⇒ finance everyone, and reduce repayment terms such that Π = γ.

25

Equilibrium under Competition (II)

The equilibrium has three cases:

1. competition does not matter⇒ monopolistic allocation, repayment terms (R, r).

2. there is threat of entry, but by adding some negative NPV projectsnoncontestability can be restored⇒ cross-subsidized excessive lending, repayment terms (R, r).

3. there is threat of entry, and even by financing all projects at terms(R, r) the incumbent does not regain noncontestability⇒ finance everyone, and reduce repayment terms such that Π = γ.

25

Equilibrium Credit Mass

mEλ(q, γ) =

1 if 0 ≤ λ ≤ 2(p̄−q)ε

and p̄ − γR−r

< q < p̄

0 if 0 ≤ λ ≤ 2(q−p̄)ε

12− q−p̄

λεif 2|q−p̄|

ε< λ ≤ 2(q−p̄)

ε+ 4γ

ε(R−r)

1−2(q−p̄+ γ

R−r )λε

if 2(q−p̄)ε

+ 4γε(R−r)

< λ < 1 and q > p̄ − γR−r

1 for all λ ∈ [0, 1) if q ≤ p̄ − γR−r

26

Equilibrium Credit Mass

mEλ(q, γ) =

1 if 0 ≤ λ ≤ 2(p̄−q)ε

and p̄ − γR−r

< q < p̄

0 if 0 ≤ λ ≤ 2(q−p̄)ε

12− q−p̄

λεif 2|q−p̄|

ε< λ ≤ 2(q−p̄)

ε+ 4γ

ε(R−r)

1−2(q−p̄+ γ

R−r )λε

if 2(q−p̄)ε

+ 4γε(R−r)

< λ < 1 and q > p̄ − γR−r

1 for all λ ∈ [0, 1) if q ≤ p̄ − γR−r

q

λ

0 1

1

p̄ − γR−r

26

Equilibrium Credit Mass

mEλ(q, γ) =

1 if 0 ≤ λ ≤ 2(p̄−q)ε

and p̄ − γR−r

< q < p̄

0 if 0 ≤ λ ≤ 2(q−p̄)ε

12− q−p̄

λεif 2|q−p̄|

ε< λ ≤ 2(q−p̄)

ε+ 4γ

ε(R−r)

1−2(q−p̄+ γ

R−r )λε

if 2(q−p̄)ε

+ 4γε(R−r)

< λ < 1 and q > p̄ − γR−r

1 for all λ ∈ [0, 1) if q ≤ p̄ − γR−r

q

λ

0 1

1

p̄ − γR−r

26

Equilibrium Credit Mass

mEλ(q, γ) =

1 if 0 ≤ λ ≤ 2(p̄−q)ε

and p̄ − γR−r

< q < p̄

0 if 0 ≤ λ ≤ 2(q−p̄)ε

12− q−p̄

λεif 2|q−p̄|

ε< λ ≤ 2(q−p̄)

ε+ 4γ

ε(R−r)

1−2(q−p̄+ γ

R−r )λε

if 2(q−p̄)ε

+ 4γε(R−r)

< λ < 1 and q > p̄ − γR−r

1 for all λ ∈ [0, 1) if q ≤ p̄ − γR−r

q

λ

0 1

1

p̄ − γR−r

26

The First Key Result

Finding 1:

Under threat of entry, equilibrium credit mass is inefficiently large.

Its excessiveness increases with bank competition.

27

Further Comparative Statics

Threat of entry makes credit more volatile:

I the sensitivity ∂mE

∂q of credit to changes in q is twice as high underthreat of competition than under monopoly.

I the average default rate Dλ(q) decreases in q: the best loans aremade in recessions, the worst in booms

I the sensitivity ∂Dλ∂q is independent of λ, but is twice as large under

threat of competition than under monopoly.

28

Endogenous Screening Choice

Gross Profit Function:ΠEλ = γ ·mE

λ wherever competition is relevant, unchanged otherwise

Optimal Screening Precision λ∗E :

maxλ

ΠEλ − c(λ)

s.t. λ ≥ 0

29

The Second Key Result

Finding 2:

Screening precision λ∗E is chosen inefficiently low when there is threat ofentry.

Marginal returns to screening

I are strictly lower under threat of entry, and

I are zero for q < p̄ − γR−r

30

Equilibrium Allocations

p̄ − γR−r

Screening Precision

q

λ∗E

0 1

1

p̄

p̄ − γR−r

Credit Mass

q

mλ∗(q)

0 1

1

p̄

31

Equilibrium Allocations

p̄ − γR−r

Screening Precision

q

λ∗E

0 1

1

p̄

p̄ − γR−r

Credit Mass

q

mλ∗(q)

0 1

1

p̄

31

Equilibrium Allocations

p̄ − γR−r

Screening Precision

q

λ∗E

0 1

1

p̄

p̄ − γR−r

Credit Mass

q

mλ∗(q)

0 1

1

p̄

31

Equilibrium Allocations

p̄ − γR−r

Screening Precision

q

λ∗E

0 1

1

p̄

p̄ − γR−r

Credit Mass

q

mλ∗(q)

0 1

1

p̄

31

Equilibrium Allocations

p̄ − γR−r

Screening Precision

q

λ∗E

0 1

1

p̄

p̄ − γR−r

Credit Mass

q

mλ∗(q)

0 1

1

p̄

31

Lending Cycles

32

A Simple Theory of Lending Cycles

Let’s play a simple dynamic version of the model:

I play a sequence of one-shot games: periods {t, t + 1, . . . }I aggregate state qt+1 unknown ex-ante

I λ̄∗t+1 is chosen before knowing the actual realization of qt+1:

maxλ̄

∫ΠEλ̄

(q, γ)− c(λ̄)dU(q)

s.t. λ̄ ≥ 0

33

Lending Cycles (cont.)

Dynamic Model (cont.):

I I use the following stylized specification:

qt+1 =

{qt with probability φ∼ U(p̄ − ε

2 , p̄ + ε2 ) with probability 1− φ

I special case φ→ 1 restores the baseline model

I Let’s think of φ as large but not quite 1, i.e. φ = 0.8

I the optimal screening precision choice problem becomes

maxλ̄t+1

φΠEλ̄t+1

(qt , γ) + (1− φ)

p̄+ ε2∫

p̄− ε2

ΠEλ̄t+1

(qt+1, γ) ε−1dqt+1

− c(λ̄t+1)

s.t. λ̄t+1 ≥ 0

34

Dynamic Screening Choice

Ex-ante Optimal Screening Choice λ̄∗E ,t+1

p̄ − γR−r

qt

λ̄∗t+1

0 1

1

p̄

35

Dynamic Screening Choice

Ex-ante Optimal Screening Choice λ̄∗E ,t+1

p̄ − γR−r

qt

λ̄∗t+1

0 1

1

p̄

35

Flight to Quality

Credit Contractions and Flight to Quality

I during boom, λ̄∗E ,t+1 is chosen low because good conditions areexpected to persist and threat of competition depresses informationacquisition incentives

I if actual realization qt+1 takes some high value (i.e., boom is over),competition would ex-post not have been the problem

I but inefficiently low λ̄∗E ,t+1 now results in credit contraction

I due to impaired screening precision, only outstanding projects can beidentified as credit-worthy ⇒ flight to quality

36

Relation with Empirical Findings

Related Empirical Findings:

I Berger and Udell (2004) “institutional memory hypothesis”

I Micco and Panizza (2005): competition increases creditprocyclicality

I Dell’Ariccia et al. (2008): lending standards fall upon entry of largeoutside lenders

I Ioannidou et al. (2009), Jimenez et al. (2009): risk-taking wheninterest rates are low

I Foos et al. (2009): rapid loan growth but low average interestincome, loan loss provisions spike three years ahead

37

Relation with Empirical Findings

Related Empirical Findings:

I Berger and Udell (2004) “institutional memory hypothesis”

I Micco and Panizza (2005): competition increases creditprocyclicality

I Dell’Ariccia et al. (2008): lending standards fall upon entry of largeoutside lenders

I Ioannidou et al. (2009), Jimenez et al. (2009): risk-taking wheninterest rates are low

I Foos et al. (2009): rapid loan growth but low average interestincome, loan loss provisions spike three years ahead

37

Relation with Empirical Findings

Related Empirical Findings:

I Berger and Udell (2004) “institutional memory hypothesis”

I Micco and Panizza (2005): competition increases creditprocyclicality

I Dell’Ariccia et al. (2008): lending standards fall upon entry of largeoutside lenders

I Ioannidou et al. (2009), Jimenez et al. (2009): risk-taking wheninterest rates are low

I Foos et al. (2009): rapid loan growth but low average interestincome, loan loss provisions spike three years ahead

37

Relation with Empirical Findings

Related Empirical Findings:

I Berger and Udell (2004) “institutional memory hypothesis”

I Micco and Panizza (2005): competition increases creditprocyclicality

I Dell’Ariccia et al. (2008): lending standards fall upon entry of largeoutside lenders

I Ioannidou et al. (2009), Jimenez et al. (2009): risk-taking wheninterest rates are low

I Foos et al. (2009): rapid loan growth but low average interestincome, loan loss provisions spike three years ahead

37

Relation with Empirical Findings

Related Empirical Findings:

I Berger and Udell (2004) “institutional memory hypothesis”

I Micco and Panizza (2005): competition increases creditprocyclicality

I Dell’Ariccia et al. (2008): lending standards fall upon entry of largeoutside lenders

I Ioannidou et al. (2009), Jimenez et al. (2009): risk-taking wheninterest rates are low

I Foos et al. (2009): rapid loan growth but low average interestincome, loan loss provisions spike three years ahead

37

Conclusions

Conclusions

I informational spillovers can change the effect of competition onlending substantially

I excessive lending booms occur due to a combination of lowscreening and cross-subsidized lending

I the model also explains credit contractions and flight-to-quality inrecessions

I suitable for integration in general equilibrium model to performmacroprudential analyses

I directions of future research:I empirical: screening choice under competition, lending standardsI theory: international lending booms and capital flows

38

Thank you!

39

Appendix: Closed Form Solutions (I)Monopolistic case:

c0

(λ− 1)2= b −

a

λ2

a =(R − r)(p̄ − q)2

2ε

b =(R − r)ε

8γ = a− b − c0

φ = 108a2b − 108ab2 − 108abγ − 2γ3

β =3√

2γ2

3a(φ+

√φ2 − 4γ6

)1/3+

(φ+

√φ2 − 4γ6

)1/3

3 3√

2a

λ∗1 =1

2

√√√√2 + β −4γ

3a−

2(a− 2b − γ)

a√

1− β − 2γ3a

−1

2

√1− β −

2γ

3a+

1

2

λ∗2 =1

2

√√√√2 + β −4γ

3a+

2(a− 2b − γ)

a√

1− β − 2γ3a

+1

2

√1− β −

2γ

3a+

1

2

whereby the correct solution is the root that lies in the [0, 1] interval. Back...

40

Appendix: Closed Form Solutions (II)

Competitive case:

λ∗C (q, γ) =1

1 +√

c0

δ

(2)

where δ = 2γε−1(q − p̄ + γR−r )

41

Appendix: Proof of equilibrium property (sketch)

Maximization subject to noncontestability constraint yields anequilibrium:

1. if portfolio P is noncontestable, and portfolio Q is noncontestableand symmetric, and its surplus is weakly higher, i.e. Π[P] ≤ Π[Q]then the incumbent can generate same or higher payoff for himselfby choosing Q over P.

2. for any noncontestable portfolio P there always exists a symmetricnoncontestable portfolio Q that yields weakly higher surplus

3. so, search within the class of symmetric noncontestable portfoliosyields an element for which payoff is maximal among allnoncontestable portfolios ⇒ equilibrium.

Back...

42