when Dynare does the idenfication test, can one change the order of approximation for solving the model? Or let the ask the question in a different way: what kind of order of approximation does the identification command use? Is it simple a linear approximation of the model?
If uses order=1. This implies that the only moments that are relevant for testing identification are the mean and the variances. For more on what is going on, see Iskrev (2010), JME.
So if some of the parameter are potentionally be identified by higher moments like kurtosis or skewness, the identifcation command cannot show this?
If parameters are identified by higher moments, do I have to use a higher order approximation?
No, identification by higher moments will not detected. Using higher order solutions often aid identification by parameters affecting higher moments (See e.g. Fernandez-Villaverde/Rubio-Ramirez 2007). Dynare will not able to detect this. However, note that it is not always straightforward to see which approximation order affects which higher order moments, particularly given that exogenous variables are currently only entered in Dynare with the first two moments.
You might want to check’‘Identification of DSGE models—The effect of higher-order approximation and pruning’’ sciencedirect.com/science/ar … 8915000731.
As Johannes was saying, higher-order moments as well as higher-order approximations MAY help identify your model, but Dynare’s built-in identification command only works with order=1 and only based on the first two moments. I’m still working on a Dynare implementation of the code of the above paper, but it is still some weeks away. The code will also be able to check identification via higher-order moments, e.g. if the shocks are t-distributed.