Dear all,
I am having some trouble with my historical decomposition. I referred to the post Influence of initial values on historical decomposition, which explains that large contributions of initial values are usually due to high persistence in the model.
In my case, whenever I estimate the model, at least one of the shocks tends to have a persistence parameter close to 1, and this seems to leave a large role for initial values in the decomposition.
I was wondering if you could share some insight into why this happens and how one might approach it. Would it make sense to impose tighter priors on the persistence parameters in order to reduce the role of initial values in the decomposition, or is there something else I should be considering?
Thank you very much for your help!
The reason is almost always a wrong specification of the observation equation, where the data mean and the model steady states are inconsistent. In that case, the model is forced to account for permanent deviations from the steady state with temporary shocks. That requires making the shocks (almost) permanent, i.e. forcing a unit root.
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Dear Prof. Pfeifer,
Thank you for your reply.
I understand better now, I remember you have mentioned the same thing when I asked you about the observation equations in my model in the post linked below, and you said:
“Yes, those steady states [y_obs and y]need to be roughly equal. Any deviation between the two concepts will need to be explained by shocks.”
I have since checked my steady state values, and it seems I may have been mistaken in judging them as “roughly equal.” For your reference:
| Variable |
Steady State Value |
| y_obs |
0 |
| y |
1.8548 |
| r_obs |
0.01005 |
| r |
1.0101 |
| pi_obs |
0 |
| pi |
1 |
I also have the following observation equations:
y_obs = log(y) - log(y(-1))
r_obs = log(r)
pi_obs = log(pi)
where I have demeaned the growth rate in output. Also, pi and r in my model is the gross inflation and gross interest rates, respectively.
Do you think these values can be considered “roughly equal,” or should I treat the differences as problematic?
I have also attached the data if you deem that useful.
Thank you so much,
Using log-differenced GDP in a non-linear model with stationary output variable
Data:
data.xlsx (25.1 KB)
In your data, r_obs has a mean of 0.05 and pi_obs of 0.04. That should be problematic.
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Dear Prof. Pfeifer,
Thank you so much for taking the time to check my file!
To correct this mismatch, would you recommend that (i) I demean r_obs and pi_obs further so that the sample means align with the model’s steady states or (ii) adjust the steady state block in the model so that it reproduces the sample means of the data?
If you are sure that the mean mismatch is not caused by a different problem (like time aggregation), then I would simply demean the data.
Thank you so much Professor!