Bank Risk Taking and
Competition Revisited:
New Theory and New Evidence
John Boyd, Gianni De Nicolò and Abu Al Jalal
The views expressed in this paper are those of the authors and do
not necessarily represent those of the IMF or the Federal Reserve
System.
Questions





Is there a trade-off between competition and
stability in banking?
The existing empirical evidence is mixed and theory
has produced conflicting predictions.
What are the implications of market structure for
bank asset allocations?
To date, neither theory nor evidence
We address these important policy questions
bringing to bear new theory and new evidence.
New Theory: bank asset allocation



Banks face both a “portfolio allocation problem”
and an “optimal contracting problem”
They acquire bonds and other traded securities (they
are price takers) and they lend in environments with
private information.
A causal relationship from market structure to
asset portfolio allocation is of more than
theoretical interest (what is special about banks?)
New Theory: bank asset allocation
We model both decisions by allowing banks to
invest in a default-risk- free government bond.
 We get a good deal of increased complexity for
two reasons:
A) Banks’ investment in bonds can be viewed as a
choice of “collateral” (indeed, the risk-free bond
becomes a risky asset....)
B) The asset allocation between bonds and loans
becomes a “strategic variable”

Two New Models



The (CVH) model : a) competition in deposit, but not
in loan, markets, and b) no contracting problem (e.g.
Keeley, 1990, Hellman, Murdoch and Stiglitz, 2000,
Repullo, 2004) .
Our model (BDN): a) competition in both loan and
deposit markets, and b) contracting problem (Boyd
and De Nicolo’ (2005).
In both models, lower concentration (more
banks) means more competition
New Theory: Predictions

Both models yield a negative relationship
between loan-to-asset ratios and concentration...
BUT

CVH model : negative relationship between
concentration and bank’s probability of failure
BDN model: positive relationship between
concentration and bank’s probability of failure

New Evidence
We explore the predictions of the models
empirically using two data sets:
 U.S. sample: 2003 cross-sectional sample of
about 2,500 U.S. banks
 International sample: panel data set with
bank-year observations ranging from 13,000 to
18,000 in 134 non-industrialized countries for
the period 1993-2004.

Empirical Results



A measure of bank probability of failure is positively
and significantly related to concentration.
The risk implications of the CVH model are
rejected, those of the BDN model are not.
The implications of both models for asset
allocations are not rejected, as loan-to-asset ratios
are negatively and significantly associated with
concentration.
Implications



No trade-off between banking stability and
competition
The positive relationship between competition
and willingness to lend suggests an important
dimension policy makers should consider to evaluate
costs and benefits of competition in banking
Many positive and normative analyses of regulation
based on CVH-type models should be re-examined.
CVH Model (1)

Bank Problem
P  S  SD  rB  rD ( Di  D) D   max{0, rB  rD ( Di  D) D}

NMH and MH strategies
CVH Model (2)

No-moral-hazard (NMH) strategy
(max{.}>0)

Moral-hazard (MH) strategy (max{.}=0)
Banks may or may not endogenously choose to
be default risk-free even though they have the
option of risk shifting.
 Focus on symmetric Nash equilibria in pure
strategies

CVH Model (3)




Proposition 1
(a) Either the unique equilibrium is MH
(loans/assets=1) or
(b) Unique NMH if N<N(1), multiple equilibria
(NMH or MH) if N(1)<N<N(2), and unique MH if
N>N(2)
Risk of failure increases in N
In (b), loans/assets move from 0 to 1 as N increases
BDN Model (1)

Entrepreneurs: Given a
loan rate , entrepreneurs
solve:
P  S  (S  rL )

Banks: Each bank solves
P  Di  D  rD (Li  L)L  rB  rD (Di  D)D   max{0, rB  rD (Di  D)D}
BDN model (2)

As before, NMH and MH strategies

But NOW, NMH strategies need to be distinguished


in two categories:
No provision of credit (if this is an equilibrium
outcome, we have CREDIT RATIONING)
Some provision of credit
BDN Model (3)
Propositions 2, 3 and 4
 (a): There exists economies for which for N<N(1) the
unique equilibrium is a CREDIT RATIONING
equilibrium (no lending)
 (b) For N>N(2), the unique equilibrium is MH
 Risk of failure decreases in N
 Loans/assets increases in N for N>N(3)
Evidence: Theory and Measurement




Measure of Bank Risk
Theory: probability of bank failure
Measurement: Z-score (distance-to-default)
Measure of Competition
Theory: Number of banks (homogenous firms)
Measurement: Hirschmann-Hirfendahl Indices
(HHIs).
Evidence: U.S. Sample




About 2500 U.S. banks that operate only in rural nonMetropolitan Statistical Areas
Cross-section for one period only, June, 2003.
The FRB defines a competitive market as a county
and maintains and updates HHI Indices
Within each market area the FRB defines a
competitor as a “banking facility,” which could be
a bank or a bank branch.
U.S. sample



The U.S. sample has an important, interesting
and unique feature. We asked the FRB to delete
from the sample all banks that operated in more than
one market area.
Thus, we are able to better match up competitive
market conditions as represented by the HHI and
individual bank asset allocations as represented by
balance sheet data.
Disadvantage : exclusion of many banks (all in HHI)
International sample



Panel data set of about 2700 banks in 134 countries
excluding major developed countries over the period 1993
to 2004 (Bankscope). (Bank-year observations range from
more than 13,000 to 18,000, depending on variables’
availability).
Disadvantage: bank market definitions are necessarily
imprecise, since it is assumed that the market for each bank
is defined by its home nation.
We did not include in the sample banks from the U.S.,
Western Europe and Japan, since defining the nation as a
market is problematic.
U.S. Sample Regressions

a)
b)
c)

Dependent variables:
Z-score,
loans/assets, and
Z-score components,
regressed on: county HHI, county/state specific and
bank specific controls
Robust OLS and GMM IV estimation
Results



Bank risk of failure positively related with
concentration
The ratio of loans to assets negatively related to
concentration
The positive relationship between bank risk of failure
and concentration mainly driven by the positive
relationship between concentration and ROA volatility
Z-score regressions
Equation:
Variable
Constant
3.1
Coeff.
t-Stat
86.1979 ***11.61
3.2
Coeff.
86.1979
t-Stat
***11.43
**-1.98 -0.0004254
**-2
3.3
Coeff.
54.13667
t-Stat
***4.44
HHI0
HHIhat
-0.0004254
-0.001221
***-4.42
Lnasset
Labgro
Unem
Farm
Cti
Totaly
R-squared / NOBS
F-test / p-value
RMSE / Categories
Hansen J Statistic /
Chi-sq p-value
-4.271885
***-6.7 -4.271885 ***-6.55 -1.393676
-11.75061
**-2.24 -11.75061
**-2.3 -23.91137
-0.3970404
***-2.6 -0.3970404
**-2.52 -0.0647434
5.495381
0.65
5.495381
0.61 13.39019
-1.853256 ***-3.44 -1.853256 ***-3.37 -1.586964
-9.63E-10
-0.85
-9.63E-10
-0.82 -3.75E-10
0.0994
2496
0.0994
2496
0.8269
F(7, 2443) ***14.17 F(7, 2443) ***13.18
16.069
46
16.069
46
16
-1.22
***-5.82
-0.53
*1.7
***-3.7
-0.56
2496
Regression With:
HHI100
***77.521
-0.0004176
*-1.89 -0.0004176
*-1.92 -0.0016029
1280
0.00135
***-3.59
Loans/Assets regressions
Equation:
Variable
Constant
HHI0
HHIhat
Lnasset
Labgro
Unem
Farm
Cti
Totaly
R-squared / NOBS
F-test / p-value
RMSE / Categories
Hansen J Statistic /
Chi-sq p-value
Regression With:
HHI100
7.1
Coeff.
-1.00652
t-Stat
***-4.05
7.2
Coeff.
-1.00652
t-Stat
***-4.02
-0.000022
**-2.46
-0.000022
**-2.38
0.1251959
***5.76 0.1251959
0.3951624
*1.93 0.3951624
-0.0030314
-0.48 -0.0030314
0.4441235
*1.37 0.4441235
-0.0685574 ***-2.94 -0.0685574
1.06E-10
***3.17
1.06E-10
0.1643
2498
0.1818
F(6, 2445) ***9.64 F(6, 2445)
0.60314
46
0.60314
-0.0000234
**-2.51 -0.0000234
***5.62
*1.93
-0.48
1.34
***-2.93
***3.04
2498
***9.17
46
7.3
Coeff.
-3.475892
t-Stat
***-5.82
-0.0001043
***-4.95
0.3704267
0.7170269
-0.0042706
2.262926
-0.0329497
-4.38E-11
0.1759
***6.6
***3.48
-0.7
***5.82
**-2
-0.96
2498
0.66
***153.15
6
1282
**-2.36 -0.0001477
0.00
***-8.88
ROA regressions
Equation:
Variable
Constant
HHI0
HHIhat
Lnasset
Labgro
Unem
Farm
Cti
Totaly
R-squared / NOBS
F-test / p-value
RMSE / Categories
Hansen J Statistic /
Chi-sq p-value
Regression With:
HHI100
4.1
Coeff.
-0.0047537
t-Stat
***-2.77
4.2
Coeff.
-0.0047537
t-Stat
***-2.72
1.14E-07
**1.96
1.14E-07
**1.93
0.0011648
***8.1
-0.0028384
**-2.13
-0.0000486
-1.06
0.0004837
0.22
-0.001137 ***-2.64
-1.08E-12
**-2.44
0.1704
2500
F(6, 2447) ***12.37
0.00429
46
4.3
Coeff.
0.0055916
t-Stat
1.52
2.16E-07
**1.9
0.0011648
***7.95 0.0001706
-0.0028384
**-2.03 -0.0011565
-0.0000486
-1.03 -0.0000906
0.0004837
0.22 0.0022197
-0.001137
***-2.63
-0.0014
-1.08E-12
**-2.35 -3.83E-13
0.1704
2500
0.7217
F(6, 2447) ***19.67
0.00429
46
0.0044
0.49
-0.92
**-2.49
1.1
***-12.87
-1.26
2500
***79.759
1.09E-07
*1.82
1.09E-07
*1.79
1.65E-07
1282
0.00078
1.15
Equity/Asset regressions
Equation:
Variable
Constant
HHI0
HHIhat
Lnasset
Labgro
Unem
Farm
Cti
Totaly
R-squared / NOBS
F-test / p-value
RMSE / Categories
Hansen J Statistic /
Chi-sq p-value
Regression With:
HHI100
5.1
Coeff.
-1.133522
t-Stat
***-7.59
5.2
Coeff.
-1.133522
t-Stat
***-7.44
2.54E-06
0.5
2.54E-06
0.5
-0.0779583 ***-5.95
-0.4275504 ***-3.76
-0.0104683 ***-2.87
-0.1889034
-1.04
-0.0166356
**-2.11
-3.93E-11
*-1.64
0.0884
2500
F(6, 2447) ***10.32
0.34204
46
2.93E-06
0.55
-0.0779583
-0.4275504
-0.0104683
-0.1889034
-0.0166356
-3.93E-11
0.0884
F(6, 2447)
0.34204
2.93E-06
***-5.78
***-3.93
***-2.87
-1.1
**-2.04
*-1.68
2500
***9.9
46
0.56
5.3
Coeff.
-1.510868
t-Stat
***-4.87
-1.64E-06
-0.16
-0.0467344
-0.4570842
-0.0037452
-0.1286715
-0.0189682
-3.02E-11
0.9724
-1.6
***-4.47
-1.25
-0.73
-1.55
-1.07
2500
0.35
1282
***72.009
0.00487
5.61E-06
0.46
ROA volatility regressions
Equation:
Variable
Constant
HHI0
HHIhat
Lnasset
Labgro
Unem
Farm
Cti
Totaly
R-squared / NOBS
F-test / p-value
RMSE / Categories
Hansen J Statistic /
Chi-sq p-value
Regression With:
HHI100
6.1
Coeff.
t-Stat
-5.965511 ***-39.59
0.000014
**2.28
6.2
Coeff.
t-Stat
-5.965511 ***-39.55
0.000014
**2.32
0.000014
t-Stat
***-15.22
0.000055
***4.32
0.001816
0.328419
-0.003309
-0.592511
0.084797
7.91e-12
0.9939
0.05
**2.52
-0.89
***-2.73
***6.80
0.23
2496
**2.29
0.027445
**2.12
0.027445
**2.12
0.058077
0.41
0.058077
0.42
0.003591
0.81
0.003591
0.82
-0.413164
*-1.90
-0.413164
*1.93
0.073592
**2.35
0.073592
**2.33
1.20e-11
0.38
1.20e-11
0.37
0.0884
2496
0.0858
2496
F(6, 2443) ***2.876 F(6, 2443) ***3.795
0.42817
46
0.42817
46
0.000014
6.3
Coeff.
-5.765605
**2.35
0.44
1280
***73.331
0.0036
0.000075
***5.32
International Sample Regressions






Z-score is defined at each date
Panel regressions with a) Z-score, b) loans/assets and
c) Z-score components as dependent variables,
regressed on:
country’s HHIs (Asset, Loans, Deposits)
country-specific and bank-specific controls.
Robust country fixed effects and firm fixed effects
panel regressions
All explanatory variables are lagged one year
Results



Bank risk of failure positively related with
concentration
The ratio of loans to assets negatively related to
concentration
The positive relationship between bank risk of failure
and concentration driven by the negative relationship
between capitalization and concentration, and the
positive relationship between ROA volatility and
concentration
Dependent Variable: Z-score(t)
Equation:
Independent Variables (t-1)
11.1
Coeff.
CFE
t-Stat
11.2
Coeff.
FFE
t-Stat
11.3
Coeff.
CFE
t-Stat
11.4
Coeff.
FFE
t-Stat
11.5
Coeff.
CFE
t-Stat
11.6
Coeff.
FFE
t-Stat
HHIA
-14.73
***-4.4
-11.17
***-3.0
-10.75
***-2.8
-13.36
***-3.2
-14.8
***-2.5
-15.39
**-2.1
0.001
30.11
0.334
-0.005
-0.0001
0.8
**2.3
**2.4
-1.3
-1
-0.001
13.5
-0.04
-0.007
-0.0001
-1.1
1
-0.3
-0.3
-0.4
0.001
7.877
0.354
-0.006
0.0001
0.9
0.5
**2.1
-1.3
0.4
-0.001
-11.86
0.049
-0.002
-0.0001
-1.4
-0.6
0.26
-0.4
-0.5
-1.444
***-3.3
-3.536
**-2.1
-0.061
0.06
***6.8
12195
0.016
0.416
1.2
12195
-0.142
-10.19
-0.3
*-1.7
-0.228
-8.525
-0.2
-1.1
GDPPC
LPOP
GROWTH
INFL
ER
LASSET
CIR
0.056
R2/ number of observations
Regressions with:
HHIL
HHID
17334
0.405
17334
0.056
15567
0.406
15567
-11.17
-11.8
-3.6***
-3.5***
-5.665
-9.102
-1.5
**-2.4
-5.35
-7.632
-1.5
**-2.0
-6.077
-10.87
-1.4
***-2.6
Dependent Variable: LGLTA(t)
Equation:
Independent Variables
(t-1)
11.1
Coeff.
CFE
t-Stat
11.2
Coeff.
FFE
t-Stat
11.3
Coeff.
CFE
t-Stat
11.4
Coeff.
FFE
t-Stat
11.5
Coeff.
CFE
t-Stat
11.6
Coeff.
FFE
t-Stat
HHIA
-0.327
***-5.8
-0.291
***-8.2
-0.385
***-5.9
-0.287
***-7.2
-0.62
***-6.3
-0.323
***5.4
-0.001
-0.1
0.001
***3.0
-1.438 ***-7.1 -1.124 ***-8.7
0.024
***9.3
0.02
***14.3
-0.001
-1.5
0.0001
0.8
-0.0001 *-1.8 -0.0001
-0.1
0.001
-1.924
0.023
0.001
-0.001
0.1
****-78.8
***7.5
-0.3
-1.2
-0.001
-1.763
0.018
0.0001
-0.0001
-0.8
***-12.0
***11.9
1.1
-1.5
*-1.8
***5.5
12841
0.155
-0.001
0.849
***11.3
***-5.3
12841
***-6.0
***-4.5
-0.382
-0.145
***6.1
**-2.3
GDPPC
LPOP
GROWTH
INFL
ER
LASSET
CIR
R2/ number of observations 0.168
Regressions with:
-0.298
HHIL
HHID
-1.98
18952
0.808
18952
0.187
16972
0.808
16972
-0.013
-0.001
0.211
***-5.1
***-3.4
-0.259
-0.177
***-7.1
***-4.9
-0.383
-0.302
***-5.8
***-4.6
-0.269
-0.195
***-6.1
***-4.8
-0.61
-0.449
Components of the Z-score(t)
Equation:
Dependent Variable (t)
11.1
ROA
CFE
11.2
ROA
FFE
11.3
LEQTA
CFE
11.4
LEQTA
FFE
11.5
Ln(σ(ROA)
CFE
11.6
Lnσ(ROA)
FFE
Independent Variables (t-1)
Coeff.
t-Stat
Coeff.
t-Stat
Coeff.
t-Stat
Coeff.
t-Stat
Coeff.
t-Stat
Coeff.
t-Stat
-0.2
-0.6
-0.03
-0.1
-0.224
***-3.7
-0.174
***-4.1
0.396
***3.2
0.11
1.1
GDPPC
LPOP
GROWTH
INFL
ER
0.001
0.354
-0.006
0.001
-0.0001
***3.6
0.6
-0.6
***2.6
-1.3
0.001
-1.71
0.008
0.001
-0.0001
***3.8
**-2.3
1.1
***2.6
-0.2
0.0001
0.921
-0.001
0.0001
0.0002
***3.5
***7.0
-0.5
0.4
***4.3
-0.001
0.674
0.002
-0.0004
0.005
-1.5
***6.6
0.2
-1.4
***4.1
-0.001
0.636
-0.018
0.0001
0.0001
-0.3
**2.3
***-4.7
1.2
1
0.002
0.939
-0.0013
-0.0019
0.0005
*1.7
***3.4
***-3.8
-1.5
*1.7
LASSET
CIR
R2/ number of observations
-0.127
-0.013
0.18
***5.8
***11.9
13069
-0.466
-0.041
0.563
***-6.8
**-7.2
13069
-0.233
-0.012
0.396
-54.5
***-6.9
12673
-0.202 ***-20.8
-1.207
-1.6
0.848
12673
-0.135
0.001
0.176
***17.5
***5.0
13069
-0.115
-0.008
0.623
***-4.4
***-3.5
13069
Regressions with:
HHIL
HHID
0.674
0.264
*1.9
0.8
1.073
0.617
***3.4
**2.0
-0.271
-0.218
***-4.3
***-3.5
-0.247
-0.192
0.127
0.215
1.0
*1.8
-0.207
-0.06
*-1.7
-0.5
HHIA
***-5.6
***-4.5
Conclusion



No trade-off between banking stability and
competition
The positive relationship between competition
and willingness to lend suggests an important
dimension policy makers should consider to evaluate
costs and benefits of competition in banking
Many positive and normative analyses of regulation
based on CVH-type models should be re-examined.