I tried to read the Canova and Sala (JME 2009) paper and Rato and Iskrev’s 's paper on dynare’s identification routine. Unfortunately, I do not understand them fully. In my model, the dynare’s identification test shows that all parameters are identified. Although it is comforting, I do not understand the economics behind clearly. Say, two of the total shocks belong to the financial category. I would like to understand which observable variable/s is helping me to distinguish between these two shocks. I used variables of national income accounts, one labor market, and two financial sector’s. Any clue on how should I start thinking about this?
Thanks.
Identification is about the curvature of the likelihood function. We are looking for the maximum of this function for each parameter. A parameter is not identified, if the likelihood does not change when you change the parameter (in a multidimensional context when the matrix of first derivatives is singular). In a linearized model, the likelihood function is a function of the first and second moments of the data. A parameter is identified if changing it affects at least one moment differently than the other parameters in the model.
What you seem to be looking for is not really identification (which refers to parameters). Insight on what distinguishes two shocks is usually best gained from looking at IRFs. There you can see the differential impact. Take e.g. a look at Christiano/Motto/Rostagno (2014): Risk shocks. They nicely show what distinguishes risk shocks from marginal efficiency of investment shocks.
Thanks Johannes. The Christiano/Motto/Rostagno (2014) paper provides a lot of discussions on the topic I have question on. It deserves further careful reading.
What I feel is, the experiments that can be useful is to re-estimate the model keeping financial variables off one at a time and check the various shock impacts. Looking at the current IRFs in my model, I see different patterns of initial responses of variables to the two shocks (qualitatively and quantitatively for some). Then this also indicates the two shocks are inherently different. Is it wrong to think that because the identification test indicates the parameters associated with these shocks are identified, this also resembles they are distinct in the model?
If they were not distinct, they were not identified. That is correct, but identification is for practical purposes not an either/or property. Weak identification is often also problematic and that is hard to judge from IRFS.