After linearization of model, I was confronted with the early equation in this file. Some components of this equation are invisible and unmeasurable parameters such as variance ε, h and the amount of λ. How do I calculate these values and the estimate DSGE model?
parameter.pdf (146 KB)
In this generality, your question is impossible to answer. In principle you can estimate unobserved objects from the data by making use of the model structure. But from your attachement it is not clear wheather the objects you are interested in are i) separately identifiable and ii) whether there are additional restrictions that need to be taken into account, like the sigma’s actually having a meaning as shock standard deviations in the model.
None of these can not be identified separately. For example, ε is firm-specific demand (idiosyncratic preference shocks) that sigma sign represents the variance of it. Also, there is no additional restriction.
Then you need to find the smallest parameter convolutions you can identify and then estimate them. You might want to look at identifiability of parameters in the NK Phillips curve where you can also only identify the product of parameters, but not their actual values.
How do I find the smallest parameter convolutions that can identify? What do you mean from identifiability of parameters in the NK Phillips curve? Can you explain more? If you can recommend resources for further study?
You have to sit down and use pencil and paper to see which parameters always only show up as a joint product or fraction. A typical example is the New Keynesian Phillips curve where in a linearized model the elasticity of substitution and the Calvo parameter are not separately identified (see Smets/Wouters (2007) and Iskrev (2010)). You can aid the search with Dynare’s identification command, which should tell you if your defined parameter convolutions/compound objects are still collinear.