# (conditional) variance decomposition

Dear all,

Could anyone please clarify the following questions?

1. Does the “variance decomposition” in dynare refer to “forecast error variance decomposition” (FEVD)?

2. What does “conditional variance decomposition” in dynare mean and what is its difference from the “variance decomposition”?

3. We have the “conditional variance decomposition” option in dynare, but what is the option for “variance decomposition”?

4. Does the “conditional variance decomposition” option in the estimation command mean the distribution of it while the same option in the stoch_simul command after the beyesian estimation command mean it at the calibrated value or the posterior mean (or mode? which one is correct if mh_replic=0 or >0)?

5. Does “shock_decomposition” mean the historical shock decomposition?

6. If so, can we roughly interpret “shock_decomposition” as the analysis of the past while “variance decomposition” as the forecast of the future?

Thanks!

1. Yes, it’s the forecast error variance decomposition (FEVD)
2. The first is the conditional FEVD, i.e. at a particular forecast horizon. The “variance decomposition” is the unconditional one, i.e. at horizon infinity.
3. The unconditional variance decomposition one is always computed in stoch_simul. In estimation, it will always be computed when `moments_varendo` is set.
4. In estimation, it will be the mean FEVD, i.e. the mean of the FEVD values over all parameter draws. In stoch_simul after estimation, it will be at the respective parameter set. From the manual:

[quote]After running estimation, the parameters M_.params and the variance matrix M_.Sigma_e of
the shocks are set to the mode for maximum likelihood estimation or posterior mode computation
without Metropolis iterations.
After estimation with Metropolis iterations (option mh_replic > 0 or option load_mh_file
set) the parameters M_.params and the variance matrix M_.Sigma_e of the shocks are set to the
posterior mean.
[/quote]

Thus, the first is a mean over parameter values while the second is rather at the parameter mean.
5. Yes.
6. Except for the fact that one is about first moments and the other one about second moments, you can see it this way.

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