1. Discussion of Emmanuel Farhi and Jean Tirole:
‘Collective Moral Hazard, Maturity Mismatch and Systemic Bailouts’
John Moore
Edinburgh University and London School of Economics

2. 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

3. typical bank:
t = t = t = 2
1 unit 3 units 4 units
endowment project project
input output
of which
only 2 units
pledgeable
bank i’s payoff Ui = c0 + c1 + c2

4. 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)

5. 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:
(2/R) =
storage new project
return borrowing investment
this is not first-best, because R < 1 distorts rest of economy

6. 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:
(2/R) =
storage new project
return borrowing investment
this is an equilibrium for n not too small
(it is not an equilibrium if n = 1)

7. Partial Bailout Equilibrium (indexed by c0)
each bank consumes 0 < c0 < 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 - c (2/R) =
storage new project
return borrowing investment
c0 = 0 corresponds to No Bailout
c0 = 1 corresponds to Full Bailout

8. Uncertainty
Suppose, for each bank, ex ante probability (project) =  < 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

9. Related model: suppose instead a fraction  < 1 of the banks
have a project at t = 1
below some critical *, full bailout ceases to be an equilibrium;
in range 0 <  < *:
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)

10. 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