endogenous variables of the model. We can make an economic interpretation of the model, before
we focus on the possibility of chaotic behaviour. Nevertheless we can observe some dynamics that
could potentially be chaotic if we drop the stability assumption.
This is the approach we follow.
With the dynamic solution of the stable model, we can analyze the economic behaviour behind
the dynamic model. We choose the impulse response function for this task.
5.3 Some dynamic properties of the simplified model
We propose several exercises that illustrate the dynamic characteristics of this simplified conflict
model. In order to do that, we define the "baseline model" as the simplified conflict model with the
following characteristics:
• The valuations follow the simple auto-regressive process
vt+1 = «' (vi)'-ρ, + ⅛1
that does not depend on the success rate.
• The depreciation of conflict technology is given by
` (si) = δi
and does not depend on the success rate.
• We make use of the following calibration:
|
σι |
σ2 |
ηι |
П2 |
δ1 = δ2 |
βi = β2 |
PR |
R |
Pi = P2 |
Pi = P2 |
Vi = V2 |
|
2 |
5 |
2 |
ι |
0.03 |
0.98 |
0.98 |
1 |
0.50 |
0.50 |
1 |
We make this assumptions because we are interested in assessing which mechanism is important for
the dynamics of the model: the valuation evolution, the adaptation to harder environment, or both.
5.3.1 Impulse response in the baseline model
First we want to analyze the effects of exogenous changes in the valuation for the conflict good in
the conflict with the simplest dynamic response. Therefore we solve the "baseline model" and study
a shock in the resource Rt, in the in vestment zt1 and in the valuat ions of one agent v2.
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