Discussion of "A positive analysis of bank
behaviour under capital requirements"
Authors: Saleem Bahaj and Frédéric Malherbe
Discussant: Sergio Vicente (Universidad Carlos III de Madrid)
First Conference on Financial Stability
Banco de España-CEMFI
May, 2017
THE PAPER
Research Question
Question
I
Theory: Propose a positive analysis of a bank’s response to
capital requirements accounting for risk-shifting and
debt-overhang
I
Empirics: Banks’response to higher capital requirements: cut
lending when prospects are low, raise equity when prospects
are high
The mechanism
Bank’s pro…ts (initial shareholders)
Π (x, z ) =
z
d s (Dividend /Capital Iss .)
}|
e
|{z}
Initial equity
+
ZA H
A NotDefault
2
γ (x + z )
| {z }
{
Capital investment
Upside Payo¤
6z
4 (X + Z )
| {z }
Loan revenue
3
}|
{7
(1 γ) (x + z )5 f (A) dA
|
{z
}
Deposits
Bank’s pro…ts rewritten
Π (x, z ) = e +
ZA H
AL
|
+
A NotDefault
Z
|
AL
2
6z
4 (1
|
2
4 (X + Z )
| {z }
Loan revenue
3
(x + z ) 5 f (A) dA
| {z }
Loan investment
{z
}
ECONOMIC SURPLUS
Shortfall
}|
γ ) (x + z )
{z
}
Deposits
{z
3
{7
(X + Z ) 5 f (A) dA
| {z }
Loan revenue
DEPOSIT INSURANCE SUBSIDY
}
Bank’s lending decision
ZA H
AL
|
∂X
(A, x ) 1 f (A) dA
∂x
{z
}
ECONOMIC SURPLUS MAXIMIZATION
+
A NotDefault
Z (x ,Z )
|
AL
(1
γ)
∂X
(A, x ) f (A) dA
∂x
{z
}
DISTORTION
=0
First-best
ZA H
AL
|
∂X
∂x
A, x FB f (A) dA =
{z
Expected loan revenue
}
1
|{z}
Cost of funds
First-best
Role of deposit insurance and limited liability
E¤ect of deposit insurance and limited liability
ZA H
ANotDefault (x)
|
one for one
capital only
z }| { z
}|
{
∂X
(A, x ) f (A) dA = π (x ) 1 + (1 π (x )) γ
|
{z
}
∂x
Expected cost of funds
{z
}
Expected mrgnl . loan revenue
E¤ect of deposit insurance and limited liability
Role of limited liability and deposit insurance
I
Bank’s limited liability (no internalization of losses) and
deposit insurance (bank’s risk not priced): bank’s funds are
subsidized
I
Negative NPV loans funded: bank does not internalize all
the downside (risk-taking–overlending in the model)l)
Role of legacy assets
E¤ect of legacy assets with defaulting states
ZA H
ANotDefault (Z)
∂X
(µ, x ) f (A) dA = π (Z ) 1 + (1 π (Z )) γ
∂x
E¤ect of legacy assets with defaulting states
∂X
(µ, x ) f (A) dA = 1 +
|∂x
{z
} |
Mrgnl .new loan revenue
1
π (Z )
{z
1
γ
}
Expected cost of funds
No legacy assets and safe new loans
E¤ect of legacy assets with defaulting states
Role for legacy loans with defaulting states
I
Non-performing legacy loans (debt-overhang): loan
revenues towards paying "inherited" deposits shortfall
I
Positive NPV loans funded: bank does not internalize all the
upside (underlending in the model)
All e¤ects together
I
Non-separabilities make it hard to tell!
Role of capital requirements and bank response
I
Substitute deposits for capital: lessen the wedge between
bank’s pro…ts and economic surplus
I
Increase capital requirements leads to...
I
Curtail lending, if overlending
I
Increase lending (raise more capital) if underlending (when
large amount of legacy loans are expected to misperform)
The empirics
Role of capital requirements and bank response
I
Bank response to capital requirements elevation leads to...
I
Cutting lending if economic prospects (low con…dence) are
bad
I
Raise capital if economic prospects are good
COMMENTS
1. From a positive analysis to a
normative theory
Optimal capital requirement?
I
Paper proposes a positive analysis of bank’s behavior under
capital requirements
Optimal capital requirement?
I
Paper proposes a positive analysis of bank’s behavior under
capital requirements
I
What would it be the optimal capital requirement in this
model?
Optimal capital requirement?
I
Paper proposes a positive analysis of bank’s behavior under
capital requirements
I
What would it be the optimal capital requirement in this
model?
I
Lack of appropriate social welfare function, but suggestive of
economic surplus maximization
Optimal capital requirement?
I
Paper proposes a positive analysis of bank’s behavior under
capital requirements
I
What would it be the optimal capital requirement in this
model?
I
Lack of appropriate social welfare function, but suggestive of
economic surplus maximization
I
In this case, γ = 1: full internalization (no deposit insurance
subsidy, no legacy liabilities paid to depositors)
Optimal capital requirement?
I
Paper proposes a positive analysis of bank’s behavior under
capital requirements
I
What would it be the optimal capital requirement in this
model?
I
Lack of appropriate social welfare function, but suggestive of
economic surplus maximization
I
In this case, γ = 1: full internalization (no deposit insurance
subsidy, no legacy liabilities paid to depositors)
I
If capital is socially costly (substituting valuable deposits for
capital): γ < 1
Cutting lending, Which message? Should we worry?
I
What is the social cost of cutting lending as a response to
increasing capital requirements?
Cutting lending, Which message? Should we worry?
I
What is the social cost of cutting lending as a response to
increasing capital requirements?
I
Cutting lending not a problem: closer to the e¢ cient
outcome!
2. Raising equity instead of cutting
lending
Same expected payo¤ to depositholders and equityholders?
I
In the model, the expected payo¤ to depositors and
equityholders is the same: higher payo¤ to equityholders
only to compensate for probability of default
Same expected payo¤ to depositholders and equityholders?
I
In the model, the expected payo¤ to depositors and
equityholders is the same: higher payo¤ to equityholders
only to compensate for probability of default
I
What if raising equity is more costly in expectation? Scarcity
rents to equityholders?
Same expected payo¤ to depositholders and equityholders?
I
In the model, the expected payo¤ to depositors and
equityholders is the same: higher payo¤ to equityholders
only to compensate for probability of default
I
What if raising equity is more costly in expectation? Scarcity
rents to equityholders?
I
Scarcity rents more likely in bad times: raising capital more
costly in bad times
Same expected payo¤ to depositholders and equityholders?
I
In the model, the expected payo¤ to depositors and
equityholders is the same: higher payo¤ to equityholders
only to compensate for probability of default
I
What if raising equity is more costly in expectation? Scarcity
rents to equityholders?
I
Scarcity rents more likely in bad times: raising capital more
costly in bad times
I
Cutting (positive NPV!) lending in bad times even in the
presence of underlending (exacerbate the problem!)
Empirical implications of costly capital in bad times
I
Cutting lending in bad times may have been a response to
increased capital requeriments due to the cost of seasoned
equity o¤ering in bad times
4. Tightening the connection
between theory and empirics
Testing empirical implication of the model
I
Empirical implication of the model:
Testing empirical implication of the model
I
Empirical implication of the model:
I
Raising capital requirements would lead to raising equity and
to cut lending in the presence of troubled legacy-assets
Testing empirical implication of the model
I
Empirical implication of the model:
I
I
Raising capital requirements would lead to raising equity and
to cut lending in the presence of troubled legacy-assets
Empirical test (bank-level):
Testing empirical implication of the model
I
Empirical implication of the model:
I
I
Raising capital requirements would lead to raising equity and
to cut lending in the presence of troubled legacy-assets
Empirical test (bank-level):
I
Banks with a higher share of troubled legacy-assets
relatively cut lending less and raise more equity
Testing empirical implication of the model
I
Empirical implication of the model:
I
I
Raising capital requirements would lead to raising equity and
to cut lending in the presence of troubled legacy-assets
Empirical test (bank-level):
I
Banks with a higher share of troubled legacy-assets
relatively cut lending less and raise more equity
I
May want to look into (ex-post) proportion of loans
written-o¤ to appraise troubled legacy-assets
5. Alternative explanations of
empirical …ndings
Better prospects may make raising equity more pro…table
than cutting lending
I
All loans perfectly correlated, fail with probability 1
I
I
Expected cost of funds with a capital requirement γ:
π + (1 π ) γ
Project expected return if not fail: H (high) or L (low), with
probabilities p and 1 p
I
I
π
Expected return [pH + (1
p ) L] π
If H high enough and L low enough, raise equity if p high
(good prospects?) and cut lending if p low (bad
prospects?)
Better economic conditions may ease raising capital
I
In good times, equity may be cheaper to raise (scarce
equity argument)
I
In good times, banks may …nd it easier to retain earnings to
increase capital
I
Data about earnings and dividends?
Controlling for demand
I
Control for …rm fundamentals (demand)
I
Identi…cation through multiple borrowing from the same …rm
at the same time (credit registry data!)
CONCLUDING REMARKS
Overall impression about the paper
I
Theory challenges common wisdom that raising capital
leads to cut lending
I
First time to see nice integration of deposit insurance
(risk-shifting) and legacy assets (debt overhang)
I
Pathway to a normative theory of optimal capital requirements
and deposit insurance?
I
Empirical analysis documenting di¤erent response of banks
to raising capital requirements: cut lending only when
economic prospects are bad
I
Policy implications:
I
Legacy asset important issue when thinking of capital
requirements (lesson from theory)
I
Economic prospects important issue when thinking of
capital requirements (lesson from empirics)