Discussion of Emmanuel Farhi and Jean Tirole:

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Discussion of Emmanuel Farhi and Jean Tirole
Collective Moral Hazard, Maturity Mismatch and
Systemic Bailouts John Moore Edinburgh
University and London School of Economics
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3 periods t 0, t 1, t 2 one good,
storable one-for-one (in
laissez-faire, gross interest rate 1 between
periods) n banks i 1, , n
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typical bank t 0 t 1 t 2
1 unit 3 units 4 units endowment project pr
oject input output
of which only 2 units
pledgeable bank is payoff Ui c0
c1 c2
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Government policy instrument storage can be
taxed (with associated lump-sum subsidy) in
particular storage at t 1 can be taxed to
reduce (below 1) the gross interest rate R
between t 1 and t 2 rest of economy has
payoff V V(R) maximized at R 1
(laissez-faire) Government welfare V
?(U1 Un)
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Full Bailout Equilibrium (? not too small) each
bank consumes endowment at t 0 c0
1 government lowers R to 2/3 at t 1 ? each
bank is able to borrow 3 units to finance
project 0 (2/R)
3 storage new
project return borrowing
investment this is not first-best,
because R lt 1 distorts rest of economy
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No Bailout Equilibrium (? not too large) each
bank stores endowment at t 0 c0
0 government leaves R 1 at t 1 each bank
uses stored endowment to supplement new
borrowing in order to finance project 1
(2/R)
3 storage new project return
borrowing investment this is an
equilibrium for n not too small (it is not an
equilibrium if n 1)
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Partial Bailout Equilibrium (indexed by
c0) each bank consumes 0 lt c0 lt 1 and stores 1
c0 at t 0 government sets R 2/(2 c0) at
t 1 this enables each bank to finance project
1 - c0 (2/R)
3 storage new project
return borrowing investment c0
0 corresponds to No Bailout c0 1 corresponds
to Full Bailout
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Uncertainty Suppose, for each bank, ex ante
probability (project) ? lt 1 and a bank
can choose whether to correlate with other
banks in any bailout equilibrium (partial
or full), banks will choose to correlate
perfectly interpreting project as crisis
liquidity injection, we see that banks
correlation here creates/exacerbates systemic
crisis
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Related model suppose instead a fraction ? lt 1
of the banks have a project at t
1 below some critical ?, full bailout ceases
to be an equilibrium in range 0 lt ? lt ?
as ? rises, the set 0, c0 for which there
exists a partial bailout equilibrium
expands this comparative static result
(arising from the strategic complementarities
between banks) can be expressed as the
probability/severity of crisis increases (?
rises), banks may decrease their
liquidity (1 c0 falls)
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• Alternative policy instruments
• minimum liquidity requirement banks must
  maintain storage
• (1 unit) between t 0 and t 1
• bailout individual banks
• this avoids distorting interest rate R
  in rest of economy
• (although raising taxes may be worse),
• but the government may not know which banks
• really need bailing out