Psychological Aspects of Market Crashes

Proposition 3 Consider any equilibrium such that Constraint (4) does not
bind for every agent. Fix also ε > 0 and consider any history st . There
exist positive constants γ < 1 and δ < 1 such that if w^st ≤ γ for some
^wst-1

predecessor st-1 of st, and if P_sⁱ_t > δ for every i, then an ε-crash occurs in
history st .

Proposition 3 states that, for any given crash magnitude, one can find
regions of parameters on endowment drop and drop anticipation sustaining
this crash. For this result to occur, agents must not be wealth-constraint
in equilibrium. The intuition of this result is given in the Introduction. A
natural case where the wealth constraints do not bind in equilibrium for
every agent is when markets are complete, as a straightforward consequence
of Theorem 3.3 in Hernandez and Santos (1996).

Proposition 3 implicitly states that an endowment drop alone may not
sustain a crash. For a crash to happen, two other conditions must be met.
First, there must be high enough individual anticipations about an endow-
ment drop next period; second, this sentiment must be shared by every agent
in the economy. It will appear clearly in the next section that, when those
conditions on anticipations are not met, an endowment drop alone may not
sustain a crash.

Quantifying the relationship between the parameters γ and δ sustain-
ing an arbitrary magnitude of crash is a central question of our analysis.
Making this link explicit in our general setting would lead to a very com-
plex and cumbersome technical analysis. Instead, we give next section the

12

<<   9   10   11   12   13   14   15   >>

More intriguing information