Non-Gaussian Shocks
Posted: Thu Jun 21, 2012 5:34 pmHi,
I'm trying to introduce skewed shocks in a basic RBC model. Summarizing some previous threads, notice that:
1. Dynare assumes that shocks are Gaussian (i.e., zero skewness)
2. For 1st and 2nd order simulations, it makes no difference whether the distribution is skewed or not, because only the first and second moments of the shocks distribution enter the approximation formula. The difference would appear when you are doing a 3rd order simulation -- which Dynare can do.
3. Nonetheless, nothing prevents you from considering arbitrary nonlinear transformations of the (gaussian) shocks.
I consider the basic RBC model (from Dynare examples page, http://www.dynare.org/documentation-and-support/examples) and I modify it to include skewed shocks.
In particular, I make use of the fact that if eps~N(0,1), then nu = (eps^2 + eps^2 ) is distributed as a Chi-Squared with 2 degrees of freedom; and therefore e = (nu - 2)/(4) is distributed as a Chi-Squared, with zero mean, unit standard deviation, and positive skewness.
Finally, I substitute the normally distributed shock to labour-augmenting technology with its non-linear transformation. Therefore, by shocking eps, one could be able to observe the impulse responses to the non-Gaussian technology shock e.
The problem is that when I run the model, Dynare is not able to find the steady state. Why is that the case? I thought that, given that e has zero mean, the steadty state would not change. Am I wroing? Any help is highly appreciated.
Best,
Ambrogio
I'm trying to introduce skewed shocks in a basic RBC model. Summarizing some previous threads, notice that:
1. Dynare assumes that shocks are Gaussian (i.e., zero skewness)
2. For 1st and 2nd order simulations, it makes no difference whether the distribution is skewed or not, because only the first and second moments of the shocks distribution enter the approximation formula. The difference would appear when you are doing a 3rd order simulation -- which Dynare can do.
3. Nonetheless, nothing prevents you from considering arbitrary nonlinear transformations of the (gaussian) shocks.
I consider the basic RBC model (from Dynare examples page, http://www.dynare.org/documentation-and-support/examples) and I modify it to include skewed shocks.
In particular, I make use of the fact that if eps~N(0,1), then nu = (eps^2 + eps^2 ) is distributed as a Chi-Squared with 2 degrees of freedom; and therefore e = (nu - 2)/(4) is distributed as a Chi-Squared, with zero mean, unit standard deviation, and positive skewness.
Finally, I substitute the normally distributed shock to labour-augmenting technology with its non-linear transformation. Therefore, by shocking eps, one could be able to observe the impulse responses to the non-Gaussian technology shock e.
The problem is that when I run the model, Dynare is not able to find the steady state. Why is that the case? I thought that, given that e has zero mean, the steadty state would not change. Am I wroing? Any help is highly appreciated.
Best,
Ambrogio