Variance decomposition

Dynare help (legacy posts)
1

Hi, can someone please tell me the default horizon of the variance decomposition in dynare. Can it be changed?

2

Dynare only report asymptotic decomposition. There is a standing request to also provide finite horizon variance decomposition

best

Michel

3

I need help in understanding what the asymptotic variance decomposition as “produced” by Dynare is. Can I interpret it as the fraction of the variance of each variable that each shock would explain in an inifinitely long simulation of the specified model (e.g. with posterior distribution of parameters (relationships as well as shock variances).

Or should I interpret it as the forecast error for the infinite time horizon? (i.e. with no new shocks)

I’d greatly appreciate fast help on this issue.

4

The first interpretation is correct. Shocks are supposed to happen in every period between now and infinity, not only once.

It is simply the decomposition of the unconditional variance of the endogenous variables

Best

Michel

5

Could someone please provide the formula for computing the asymptotic variance decomposition? I have difficulty understanding how it is computed.

[quote=“KarlWalentin”]I need help in understanding what the asymptotic variance decomposition as “produced” by Dynare is. Can I interpret it as the fraction of the variance of each variable that each shock would explain in an inifinitely long simulation of the specified model (e.g. with posterior distribution of parameters (relationships as well as shock variances).

Or should I interpret it as the forecast error for the infinite time horizon? (i.e. with no new shocks)

I’d greatly appreciate fast help on this issue.[/quote]

6

After solving the linear rational expectation model, the solution has the form

y(t) = Ay(t-1)+Bu(t)

where y is measured in deviation to its steady state. Assuming stationarity (this is warranted by Blanchard and Kahn conditions in the absence of unit root), the variance satisfies

Sigma_y = ASigma_yA’ +BSigma_uB’

This is a Lyapunov equation in Sigma_y that is solved in Dynare with an algorithm specialised for this type of equation.

Best

Michel

7

Thanks a lot!