main quantitative features of this relationship in the well-known framework
of Mehra and Prescott (1985) through numerical simulations. The choice
of this framework is motivated by tractability reasons, and also for its large
impact in terms of macroeconomic analysis.
4 Numerical simulations
We now carry out some numerical simulations to find regions for the pa-
rameters described in Proposition 3 sustaining arbitrary levels of crashes.
We narrow down our model to that in Mehra and Prescott (1985), with the
difference that we do not assume any condition on the endowment process
and we allow for arbitrary beliefs. Our first simulation gives a region for
the parameters δ and γ sustaining a given crash magnitude for various lev-
els of risk-aversion. The second simulation shows that, for a given level of
endowment drop this time, the higher the anticipation the higher the crash
magnitude. The third simulation is a 3D-representation of crash magnitudes
as a function of both drops and anticipations, illustrating the intuitions given
in the Introduction.
We now assume, following Mehra and Prescott (1985), that in every pe-
riod two states only can occur. We also assume that there is one agent only
within the economy (a representative agent) forming subjective belief about
economic uncertainty. Even if strong in appearance, this last assumption has
already been largely justified in terms of macroeconomic analysis. Proposi-
tion 3 still remains relevant in this setting, the only conceptual loss is that it
13
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