Discussion of Emmanuel Farhi and Jean Tirole:

‘Collective Moral Hazard, Maturity Mismatch and Systemic Bailouts’

John MooreEdinburgh University and London School of Economics

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

typical bank:

t = 0 t = 1 t = 2

1 unit 3 units 4 unitsendowment project project input output

of which only 2 units pledgeable

bank i’s payoff Ui = c0 + c1 + c2

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)

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 < 1 distorts rest of economy

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)

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 - c0 + (2/R) = 3

storage new project return borrowing investment

c0 = 0 corresponds to No Bailout c0 = 1 corresponds to Full Bailout

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

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)

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