# Initial value and shock decomposition?

Hi,
Please can anybody tell me what the initial value in the graph for shock_decomposition stands for? It ain’t part of the shocks i provided but there it is in the graph unexplainable!!!

Olayeni

The solution of a linear rational expectation model is a VAR whose coefficients are constrained to satisfy the restrictions implied by the structural equations.
As any VAR, its dynamics will be to return to equilibrium. Then, the trajectory of endogenous variables is affected by how far from the steady state the system was at first (initial conditions) and the shocks arriving subsequently.
So, in the decomposition, we need to keep track of initial conditions so that the sum of the effects in the graph sums up to the endogenous variable (less its steady state).

Best

Michel

Thank you Michel

HI，
I want to ask a question about the usage of “shock_decomposition” command in Dynare. In the output of this command, besides the individual contribution of the shocks, I also get a series for “initial values”.
Can you tell me how to eliminate the impact of the initial value? What is the command to complete it?

``Thank you very much for the answers in advance``

There is no way to get rid of the initial values. You don’t know at which values for the states your system started as they are unobserved. There always remains some residual uncertainty about the initial values of the system.

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I have a question on the shock decomposition command. How are the initial conditions set? I thought they were at the steady state but obviously that is not the case because they wouldn’t have any contribution at all. Can anyone help me with this? Thanks

They are not set, but deduced. The Kalman smoother works backwards in time and finally ends up estimating the best guess for x_{0|T}, that is the best estimate for states at time 0 given all the observed data. In general, the estimate will be different from the steady state, because the data did not start in steady state.

Consider a two-period model where you have a mean 0 AR(1) process with autocorrelation 0.95 and a standard normal shock. Assume you observe a value of 3 in the second period and you do not know the initial value. What is more likely? That a three-sigma shock happened and the system was at steady state initially? Or that a small shock happened and the system was already above 0 when time started (essentially meaning there were positive shocks before time started and due to the persistence those effects can still be seen today)? The Kalman smoother for its class of problems optimally trades off these two considerations. If persistence is not high, the deviation from steady state due to the initial state will die out quickly.

This is great, thank you very much for the fast response !