I’ve tried searching the forums and looking in various books (Durbin & Koopman 2012 and Hamilton 1994) but haven’t been able to find what I’m searching for so I’ll just ask it here.
How should I interpret the size and sign of the shocks in the historical shock decomposition graph produced by the command shock_decomposition;? I tried looking at Pfeifer’s introduction to graphs but it doesn’t mention size/sign.
I’ve attached an example below where a shock decomposition is made for consumption. If we take the monetary policy shock (eta_R) as an example, we see that there are large positive spikes from around period 50-70. Does this mean a positive interest rate shock (i.e. higher interest rates) where the magnitude is indicated by the y-axis? As such, would the interpretation be that the fall of smoothed consumption deviations from steady state (model is log linearised around S.S) can be explained by a positive monetary policy shock. Secondly, can the magnitude of shocks then be compared to the prior/posterior standard deviations of the shocks?
I think you are confusing something. What is depicted is not the smoothed shocks, but the joint contribution of a particular type of shock to deviations of a variable from its mean. The problem with the interpretation is that even one-time shocks introduce dynamics over time. Say your monetary policy shock has a hump-shaped IRF with overshooting, i.e. it switches from a positive output response to a negative on after say 20 periods. If you now observe output being above steady state, this could in principle result from either a negative monetary policy shock 20 periods ago or a contemporaneous positive monetary policy shock. Due to thes temporal dynamics, just observing the shock decomposition does not allow you to infer single shocks at a point in time (that is what the Kalman smoother does). Rather, the shock_decomposition graph shows you the sum of all effects of current and past shocks.
I have more or less the same ‘problem’. Pleas have a look at my pdf. I can get that the epsilonpsi follows the deviations of the observed variable from it’s mean, but what about the others shocks? For example the epsilongammas doesn’t follow at all these deviations.
Secondly, do the axis have a meaning for the shocks on this graph or its only the observed variables concern? I mean does it say something that the epsilongammas goes up to 0.8?
The contribution for different shocks can go into opposite directions. Only their sum must add up to the observed series. Your picture looks quite strange in this regard. You have massive swings caused by shocks that tend to cancel each other. Often, this is a sign of model misspecification as the model is not capable of explaining the data without correlated shocks in-sample.