Identification of the shocks

Identification/Sensitivity
1

Hello everyone,

I would like to understand how which observables should I select to identify an specific shock. I guess that the answer is straighforward if we want to identify a TFP shock. Nevertheless, for example in the case of news shocks how can I know before getting the results of the estimation if I am going to be able to identify them with an specific set of observables.

Is it just intuition and a trial and error process?

Thank you very much in advance

2

You need to distinguish between identification per se and weak identification. Identification per se usually refers to being able to estimate parameter values at all, given a data series at hand. Dynare allows you to conduct this check using the identification-command. This is a theoretical property.
What you have in mind is different, i.e. which data series are informative to infer the shock realizations. There is no good guidance here. It is indeed trial and error (and intuition). Sometimes, the theoretical IRFs already give you a good guidance. If the shape of IRFs for a particular variable differs a lot across shocks, it is likely to be informative.

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Thank you very much, really helpful

4

Hi Prof. Pfeifer, may I kindly ask somethings related to the identification of structural shocks in macro models in general, thus DSGEs and VARs.

  1. sometimes identification of structural shocks appears to be mean simply making the structural residuals or shocks (e_t) of a model uncorrelated. In DSGE models, the independency of shocks is imposed (sometimes not). In SVAR models, people sometimes use the following definition u_t = Be_t, where e_t's are assumed to be uncorrelated.

QUESTION: So if some e_t's are assumed to be correlated in ‘structural/theoretical’ DSGE models, maybe to match certain correlations in the data, are they still considered structural given that they are assumed to be correlated?

  1. Other times, identification of structural shocks also appears to mean finding an economic interpretation for the e_t's. People sometimes just impose an economic meaning on the e_t's. Other times, as in Gali (1999), for example, he rigorously shows that e_t (which is productivity shock in his model) specifically means technology shock (z_t) and not any other shock.

QUESTION: So it appears there could be stages in the identification of structural shocks, right? For example, first, we can identify productivity shock (e_t) from the other shocks in the model (as in making e_t's uncorrelated). Second, we can identify technology shock as the sole productivity shock (as in Gali(1999) based on some assumptions). And perhaps, we can go even further to identify, say weather shock as the sole technology shock depending on the model and some assumptions, right? And so on till we get some economic meaning for e_t.

Or maybe the above is rather structural identification that should be distinguished from normal identification? In Stock and Watson (2002), for example, they mention a Cholesky-factored VAR without structural identification leading to a difficult interpretation of the shocks.

So like structural shocks in a Cholesky-factored VAR are identified but not structurally identified (i.e., no specific meaning for the structural shock), right? Many thanks for the time.

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  1. Structural identification in the context of a VAR must not be confused with the identification of parameters that is done in the identification-toolbox.
  2. The underlying problem is that the Covariance matrix is symmetric so that it does not uniquely identify a mapping from structural shocks to residuals. The mapping matrix B in your notation has n^2 entries, but the covariance matrix \Sigma=E[Bee'B'] only defines n(n-1)/2 separate restrictions. That’s why you need identifying assumption like Galí did or simply a Cholesky decomposition.
  3. It’s strictly speaking not necessary to impose uncorrelated shocks. Any covariance matrix for the structural shocks E(ee’) would be valid. It’s simply convenient to assume it’s the identity matrix.
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