Financial Intermediation

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Financial Intermediation

• Lecture 5
• Competition in Banking

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Competition issues

• Cournot competition once again
• Double Bertrand competition
• The Salop model
• Tests per banking market Panzar-Rosse,
  Bresnahan-Lau and the Structure-Conduct-Performanc
  e hypothesis
• Illustration for the Dutch mortgage market

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Klein-Monti model

• Downward-sloping demand for loans L(rL)
• Upward sloping demand for deposits D(rD)
• We will use the inverse functions rL(L) and rD(D)
• Maximize ?(L,D)rL(L)LrM-rD(D)D-C(D,L). There is
  e.g. an impact of L on rL
• M(1-a)D-L, so
  ?(L,D)(rL(L)-r)L(r(1-a)-rD(D))D-C(D,L).

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Klein-Monti (2)

• Assume the profit function is concave
• FOC1 rL(L)LrL-r-CL(D,L)0
• FOC2 -rD(D)Dr(1-a)-rD-CD(D,L)0
• Define the following elasticities
  eL-rLL(rL)/L(rL)gt0 and eDrDD(rD)/D(rD)gt0

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Klein-Monti (3)

• We get a famous result a monopolistic bank will
  set its volume of loans and deposits such that
  Lerner indices equal inverse elasticities
• rL-(rCL)/rL 1/eL(rL)
• r(1-a)-CD-rD/rD1/eD(rD)

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Cournot competition

• Finite number of competing banks N
• The first-order conditions change into
• rL-(rCL)/rL 1/NeL(rL)
• r(1-a)-CD-rD/rD1/NeD(rD)
• Each bank sets DnD/N and LnL/N
• For N1 we get the Klein-Monti and for N infinite
  we get perfect competition!

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Double Bertrand competition

• Banks compete using interest rates.
• Bertrand competition prices are central, but
  with two banks we get perfect competition
• Idea banks compete on the markets for output
  (loans) and inputs (deposits)
• Assume constant marginal costs (normalized to
  zero)
• L(rL) demand for loans, D(rD) supply of deposits

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Double Bertrand competition (2)

• Reserve requirements ignored
• Walrasian equilibrium rLrDrt, where rt is
  simply the solution of L(r) D(r)
• Suppose now that banks first compete for deposits
  and next to that operate on the loans market.
  Offering a slightly higher rDrte creates a
  monopoly on the loans market

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Double Bertrand competition (3)

• With two banks and a relatively high loan demand
  elasticity we get (see Stahl, 1988)
• Only one bank is active.The interest margin is
  positive rLgtrD. Both banks have zero profit
  though. The active bank has idle reserves
• The loan rate rL is the one that maximizes
  (1rL)L(rL).
• The deposit rate is determined by
  (1rD)D(rD)(1rL)L(rL)
• There is excess supply of deposits L(rL)ltD(rD)

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The Salop model (1)

• The Salop model is a model of spatial
  competition banks all are on a unit circle
• Depositors have to get to the bank to get a
  high(er) return
• It is a model of monopolistic competition
  product differentiation is generated by
  transportation costs
• Is free banking optimal?

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The Salop Circle
Bank (i1)
1/n-xi
Depositor
xi
Bank i
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The Salop model (2)

• n banks 1,.,n located on the circle of length 1
• Banks get deposits and invest in a riskless
  technology with r return. Depositors cannot
  invest in this technology
• Depositor deposit in a bank at a cost ax,
  proportional to x the distance between depositor
  and the bank.
• There is a D mass of depositors

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The Salop model (3)

• Depositors are uniformly distributed
• With n banks the maximal distance is 1/2n
• Sum of all depositors transportation costs is
  2n?0½n ax Ddx aD/4n
• A setup cost of a bank is F
• The optimal number of banks minimizes nFaD/4n,
  which is n½?aD/F

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The Salop model (4)

• Free entry n banks settle on the circle and set
  deposit rate ri. How much deposits are in each
  bank?
• See the Salop circle the marginal depositor,
  indifferent to going to bank i or i1
• ri-axiri1-a(1/n-xi). Remember that the distance
  between banks is 1/n
• So xi1/2n (ri-ri1)/2a

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The Salop model (5)

• Now we integrate over the distance to get the
  total amount of deposits per bank
• DiD1/n(2ri-ri-1-ri1)/2a
• Profit bank i D(r-ri)1/n(2ri-ri-1-ri1)/2a
• Equilibrium if for all i ri maximizes profits
• r-ria/n(2ri-ri1-ri-1)/2
• This leads to r1rnr-a/n. So profits are all
  aD/n2. With costs F this leads to n?aD/F
• So free competition leads to too many banks
  there is scope for public intervention

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Competition on markets macro tests

• Structure-Conduct-Performance paradigm market
  structure influences performance of banks (more
  concentrated markets facilitate collusive
  agreements, increase market power and so
  profitability)
• Relative-Efficiency hypothesis efficient firms
  earn relatively high profits and thus increase
  market share concentration of profitable firms

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Competition on markets Panzar-Rosse test

• Panzar-Rosse formulate a revenue function per
  bank (firm) as function of input prices. The
  Panzar-Rosse H is the sum of elasticities of
  gross revenue with respect to input prices
• If Hgt0 any form of imperfect competition is
  rejected

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Competition test Bresnahan-Lau

• Conjectural variation method estimate the banks
  anticipated response of its rivals to an output
  change
• Let qi the output of bank i and Q the aggregate
  output.
• The conjectural variation elasticity
  kidQ/Q/dqi/qi
• ki0 for perfect competition, perfect collusion
  ki1. 0ltkilt1 for oligopoly

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Bresnahan-Lau (1)

• Total revenue in the banking industry is PQ(P),
  so marginal revenue is PQ dP/dQ
• Rewrite h(.)Q/(dQ/dP) is the semi elasticity of
  market demand
• For bank i it holds that it perceives marginal
  revenue by P qi dP/dqi. This is Pki h(.)

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Bresnahan-Lau (2)

• Empirical model aggregate asset demand Q plus a
  supply relation based on profit maximization
• Q a0a1Pa2Ya3Za4PZ
• P -k Q/(a1a4Z)b0b1Qb2W1b3W2
• Interaction term PZ needed for identification

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Market dominance

• I To what extend does a bank take into account a
  cost increase? If it is able to hold constant the
  Lerner-index it has market power
• II If a bank does not respond to a competitors
  price change it has market power

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Example Dutch mortgage market

• Four banks have 90 per cent of the market
• There is some evidence of full indexation of cost
  increases and waiting in transmission of cost
  decreases (asymmetric pricing)
• There is suspicion of collusion and market
  leadership

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Dutch price changes 1999 for 5-year contracts
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Asymmetry?
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Market leadership? Responses to bank As behaviour
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..and Bank Cs
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Conclusions

• Collusion at least suspected
• Asymmetry hard to establish
• Bank A is a true market leader other banks
  respond to changes in Bank As prices and hardly
  the other way round

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Background readings

• Freixas and Rochet, Microeconomics of Banking
• Toolsema, On Competition and Banking