Theory and empirics of
bank competition
Andrea F. Presbitero
Dipartimento di Economia
Email: [email protected]
Lecture outline
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Introduction on banking structure.
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Brief review of theoretical underpinnings and some empirics.
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A simple model of competition (Monti-Klein)
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Petersen and Rajan (1995): the benefits of concentration for
young firms. Theory and empirics
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Shaffer’s model of “the Winner’s curse”
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The impact of banking structure on growth (Cetorelli and
Gambera, 2001)
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Consolidation of credit markets
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In the 1990s, both European countries and US experienced a
deregulation of financial markets which increased competition through
the removal of barriers to entry.
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The liberalization of financial industry has an impact on market
structure of the banking industry.
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The EU liberalization increased cross-border competition and M&A.
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Italy experienced a great consolidation and restructuring process, with
the concentration of decisional centers in the North.
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Bank Competition: theory
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Market power reduces credit available for firms (rent extraction, higher
loan rates, inefficient allocation), hindering growth (Pagano, 1993).
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The strategy of initial “subsidization” and subsequent “participation”
is possible in not competitive markets (Petersen and Rajan, 1995) .
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Shaffer (1998) point out the “winner’s curse” problem associated with
bank competition.
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There is a trade-off between the quantity of funds supplied (size of the
credit market) and the quality of financed entrepreneurs (efficiency of the
credit market).
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Review of empirical evidence
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Bonaccorsi and Dell’Ariccia (2000): in Italy, the creation of (opaque)
firms is higher in provinces with more concentrated banking sectors.
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Cetorelli and Gambera (2001) find mixed results:
1.
2.
bank concentration has a negative effect on industry growth (cross
country).
Industries (especially younger firms) more dependent on EF grow faster
in countries where the banking sector is more concentrated.
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The relationship between banking market structure and steady state
income could not be monotonic.
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The maximizing market structure is neither a monopoly nor perfect
competition, but an oligopoly (Cetorelli, 2001).
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An imperfect competition model
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A monopolistic bank, facing a downward sloping demand curve
for loans [L(rL)] and an upward sloping supply of deposits
[D(rD)].
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The decision variables are L and D.
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Profits:
Π(L,D) = rLL + rM – rDD – C(D,L)
M=(1 – α)D – L is the net
position on the interbank rate
α is the reserve coefficient
r is the CB rate
cost function
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Solution
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From the FOCs and using the elasticities we find the equilibrium
rates r*L and r*D (Lerner index equal to inverse elasticity):
rL* − (r + C L′ )
1
=
rL*
ε L rL*
( )
1
r (1 − α ) − C L′ − rD*
=
rD*
ε D rD*
( )
Lerner indexes (prices minus marginal cost divided by
price): they area measure of monopoly market power.
Where the elasticities of the demand (supply) for loans are defined as:
rL L′(rL )
εL = −
>0
L(rL )
εD =
rD D′(rD )
>0
D (rD )
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Oligopoly
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Intermediation margins are higher the higher market power is.
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With infinite elasticities we end up with perfect competition
(intermediation margins equal to marginal costs).
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A more realistic model is the oligopolistic version: N identical
bank with the cost function:
Cn(D,L) = γDD + γLL
n=1,…,N
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Equilibrium
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Maximizing profits, so that D*n = D*/N and L*n = L*/N:
rL* − (r + γ L )
1
=
rL*
Nε L rL*
( )
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z
z
r (1 − α ) − γ L − rD*
1
=
rD*
Nε D rD*
( )
The only difference is that elasticities are multiplied by N, so:
The Monti-Klein model could be easily interpreted both as
competitive model (N→∞) and as monopoly (N=1).
The sensitivity of r*L and r*D at changes in r depends on N, which
measures the intensity of competition. As N increases, r*L (r*D)
will become less (more) sensitive to changes in r.
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Benefits of concentration
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Petersen and Rajan (QJE, 1995) propose a model in which credit
constrained firms are more likely to be financed when credit
markets are concentrated.
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The intuition is that the a monopolistic lender could start a close
relationship with the borrower. Thus, the bank will be able to
extract future rents as compensation for early subsidizing.
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Three period model with a determined amount θ of good
entrepreneurs and (1-θ) of bad entrepreneurs. The firm borrows
short term each period.
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The Petersen and Rajan model
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Other assumptions
1.
Banks are the only sources of finance.
2.
Banks will know in time t = 1 if agents are good
or bad entrepreneurs.
3.
Banks can charge a rate such that:
S2/I1S > M > 1
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Selection process
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In t = 0 good entrepreneurs (GE) could not distinguish
themselves from the bad (BE) ones. They will borrow at a higher
rate (credit rationing).
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GE will ask the minimum amount possible at t = 0.
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In t = 1 the BE are exposed and the GE can borrow the desired
amount at a lower rate.
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A GE will borrow I0, repaying D1. In t = 1 he will negotiate
another loan:
I1S – (S1 – D1)
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Solving the model
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The bank will lend only if two conditions are met:
1.
2.
The investor will choose the safe project
The bank will gain from lending
Condition 1 (moral hazard):
Expected payoff of the safe project (S):
max [S2 – M(I1S – (S1 – D1)), 0]
Expected payoff of the risky project (R):
max {p[R2 – M(I1R – (R1 – D1))], 0}
S is preferred to R if:
(S1 – pR1)/(1 – p) ≥ D1
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Condition 2 (bank’s rationality condition):
θMD1 + θM(I1S – S1) ≥ I0 + θ (I1S – S1)
Expected revenues
costs
D1 ≥ (I0/θM) – [(M – 1)/M](I1S – S1)
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Using these two conditions, we find a relation between the
quality of financed firms and banks’ market power:
θ(M) = I0(1 – p)/[M(S1 – pR1) + (M – 1)(I1S – S1)(1 – p)]
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In more concentrated markets (large M), firms with lower credit
quality will be financed
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Implications
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The first demanded repayment (D1) is lower bounded by the
rationality condition and upper constrained by the minimum
between the moral hazard condition and its market power (θD1
< I0M).
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When competition increases the lowest quality firm will face a
higher initial interest rate: from the rationality condition:
∂D1
< 0. Thus:
∂M
↓M → ↑competition → ↑credit rationing
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The empirics
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Empirical testing of the theoretical model according to which market
concentration favor lending to young or distressed firms.
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Survey data on more than 3,000 US small firms in 1987 (cross-section).
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Proxy for banks’ market power: Herfindahl-Hirschman Index (HHI)
for the market for deposits.
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HHI measures the degree of market concentration and it is defined as:
⎛
⎞
D ji
⎜
HHI i = ∑
.100 ⎟
⎜ j D
⎟
TOT _ i
⎝
⎠
2
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Hypothesis to be tested
H1
Relatively more firms should be able to obtain banking credit in
areas where credit markets are more concentrated;
H2
Credit should be cheaper for the lowest quality firm in a
concentrated market than in a more competitive one;
H3
The cost of credit should fall faster as a firm ages in a competitive
credit market than in a concentrated one.
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Descriptive analysis
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296 firms in competitive markets (HHI>1800) and 2037 in
concentrated markets (HHI<1000).
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Young and old firms are divided according to the median age of 10
years.
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The distribution of firms across industries is very similar in different
markets.
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In sum, the quality of firms in competitive markets seems to be as
good as nor better than in the most concentrated markets. Estimates
should not be biased.
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H1 Credit availability
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Young firms located in the most concentrated markets are more likely
to get capital (65% have institutional debt, against 55% of firms
located in the more competitive markets). Effect even larger for
youngest firms, less subject to survival bias.
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This is not due to the fact that firms in concentrated markets borrow
less. As firms get older, they rely more on internal financing,
consistently with the model prediction that banks will charge higher
interest rates.
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Using trade credit discount and penalties – an industry (not firm)
specific indicator of credit constraint – the authors confirm the
model’s predictions: fewer firms appear to be credit constrained in the
most concentrated markets.
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H2-H3
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Cost of credit
The descriptive analysis of the data suggest that young firms pay
higher interest rates, but the pace at which the rates decline is faster in
competitive markets.
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Multivariate analysis
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OLS regression of the loan rate as a function of firm’s age, market
concentration, and firm- and loan-specific effects.
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Interaction term between firm age (old/young) and market
concentration.
This effect is for the
average firm, there is no
evidence the lowest
quality firm obtain a
lower rate in
concentrated markets
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Loan rates across market
structures
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Results and implications
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Young firms in concentrated markets receive more credit than similar
firms in competitive markets. As firms get older, this difference
vanishes.
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Creditors seem to smooth interest rates over the life cycle of a firm in
a concentrated market.
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The most plausible explanation is the one embedded in the theoretical
model.
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The bottom line of the paper is that competition and long-term
relationship are not always compatible. On the other hand, it may be
wrong to look at the lack of competition as a costless solution.
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The Winner’s curse
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There are a number of theoretical model explaining the “winner’s
curse” in banking. It is a problem of adverse selection.
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The idea is that rejected applicants have the ability to apply at
additional banks and, if screening is imperfectly correlated across
banks, riskier applicants will eventually get a loan.
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The more the banks, the more likely is the worst borrower to be
mistaken for a good one.
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The average creditworthiness of the pool of applicants decreases
with the number of banks.
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Shaffer’s model (1998)
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z
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N borrowers (a known fraction α are good borrowers) and n banks.
Good (bad) borrowers repay a fraction θH (θL) of their loan.
r is the exogenous interest rate and: 0 < θL < θH <1
Bank’s expected profits: rθH – 1 + θH > 0
(sustainability)
(screening)
rθL – 1 + θL < 0
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Banks observe i.i.d. noisy and informative signals on a borrower. The
signal corresponds to the true type with probability:
½ < plL < 1
½ < phH < 1
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The signal can be interpreted as the results of bank’s credit screening.
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Monopolistic bank:
creditworthy applicants: phHαN + (1 – plL)(1 – α)N
rejected applicants:
(1 – phH)αN + plL(1 – α)N
expected profits:
phHαN(rθH – 1 + θH) + (1 – plL)(1 – α)N(rθL – 1 + θL)
2 banks:
They can not disentangle between previously rejected and new applicants
Additional applicants: (1 – phH)αN/2 + plL(1 – α)N/2
Loans to rejected:
phH(1 – phH)αN/2 + (1 – plL)plL(1 – α)N/2
Total loans:
phH(2 – phH)αN + (1 – plL)(1 + plL)(1 – α)N
The total loans of the two banks are larger than with a monopoly
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n identical banks:
n
Applicants per bank:
Loans per bank:
Total loans:
(α N n )∑ (1 − phH )
m =1
m −1
n
+ (1 − α )( N n )∑ plLm−1
m =1
n
( phH α N n )∑ (1 − phH )
n
m =1
m −1
phH αN ∑ (1 − phH )
m =1
m −1
n
+ (1 − plL )(1 − α )(N n )∑ plLm−1
n
m =1
m −1
lL
+ (1 − plL )(1 − α )N ∑ p
m =1
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Total loans increases with n, so that more banks means that fewer applicants
will not obtain the loan.
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phH > ½ > 1 – plL means that at each round are accepted a higher proportion
of good applicants than of bad ones (worsening pool).
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Expected loss rates are an increasing function of the number of banks.
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Expected aggregate bank profits could increase with n. Thus, assuming that
applicants increases their utility from a loan, social welfare could increase with
the number of banks
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Empirical analysis – new banks
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Adverse selection and multi-applying could be mitigated by common
filters, relationship banking, collateral requirements, application fees.
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The analysis of the charge-off rates according to banks’ age shows that
for young banks bad loans are more than fore mature banks.
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A new bank, in fact, will face the usual mix of initial and subsequent
applicants plus a backlog of rejected applicants. Thus, it will suffer a
higher loss rate than an incumbent bank.
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Number of banks
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The analysis of 3,000 banks in 1990 distributed in 300 MSA points out
that the charge-off rates are an increasing function of the number of
banks.
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The relationship is non-linear (log of number of banks better fits the
data). The impact of an additional rival bank on incumbents is larger
the more concentrated is the market.
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This effect is valid especially for commercial loans, while not for
consumer and other loan types. This could be due to common data for
consumer loans, standardized criteria and collateral requirements for
real estate and agricultural loans.
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Welfare effects and implications
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Household income in US during 1979-89 grew faster in MSA with
more banks than in areas with a limited banking sector.
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Evidence consistent with previous national studies and with cross
country analysis.
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A more competitive banking structure does not undermine economic
growth, but it constitutes a net transfer of wealth from the banking to
the real sector.
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Two main policy implications:
1. More stringent standard for chartering new banks (limit charge-off)
2. Promote local competition
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Market structure and growth
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Cetorelli and Gambera (2001) uses an approach similar to Rajan
and Zingales (1998) to estimate the effects of bank competition
on growth across industries and countries.
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The dataset is the same used by RZ. Baking concentration is
measured as the sum of market shares of the three and five
largest banks.
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In a basic growth model (dependant variable is the GDP growth
rate in country j and sector k), bank concentration has a negative
effect.
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Contrasting effects
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The regression model includes bank concentration and the
interaction between bank concentration and external dependence
of young firms (less than 10 years old).
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Bank concentration has a negative indiscriminate effect, while
the coefficient on the interaction term is positive: there is an
industry specific positive effect of concentration.
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This is theoretically consistent with the prior that market power
facilitates lending relationships and enhances growth for sector
more in need of this relations.
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Implications
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Moving from the 25° to the 75° percentile has an overall effect
of 2.6% (less growth). The industry specific effect is 0.8% (1.7%)
for the 25° (75°) percentile (more growth).
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For sectors in the upper tail of the distribution (glass, drugs) the
overall growth effect of market concentration is positive.
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For mature firms the effect is much lower, according to theory.
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From a policy perspective, there is not a Pareto-dominant policy.
Banking market structure plays an important role for cross
industry redistributive role, and for technological innovation.
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