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_posts/Economics/2020-07-26-solving_dsge_models_numerically.md

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@@ -70,11 +70,11 @@ The general approach for perturbation techniques is:
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Consider a simple DSGE model with a representative agent optimizing utility, where the Euler equation in the steady state is:
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\[
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$$
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E_t \left[ u'(c_t) = \beta u'(c_{t+1}) \right]
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\]
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$$
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A first-order perturbation would linearize this equation around the steady state values of \( c_t \) and \( c_{t+1} \), resulting in a system of linear equations that approximate the dynamics of the economy in response to small shocks.
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A first-order perturbation would linearize this equation around the steady state values of $$ c_t $$ and $$ c_{t+1} $$, resulting in a system of linear equations that approximate the dynamics of the economy in response to small shocks.
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### Advantages and Limitations of Perturbation Methods
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