Deterministic trend?

Steady state
1

Hi everyone!
I have this exchange rate equation in the model:

S = S(-1) + dS/4;

Where the steady state of dS has a value different than zero.
How can I define S in the steady state block? Is there a way to use deterministic trend ?
(I have to define it as I use it for defining the expected exchange rate also)

2

What are you trying to do? Stochastic simulations? Will the model have a steady state if properly detrended?

3

Thank you for the answer, professor.
I am doing deterministic simulations.
The idea is that, I have to provide a steady state for non-stationary variable (S, exchange rate), because I have to use it’s value in the computation of the steady state of expected exchange rate (S_exp). If I don’t include their values in the steady state, I am having residuals in expected exchange rate equation. But simply putting steady state value of S as zero or any other constant will be incorrect.
I would be happy to not fix the steady state values of S and S_exp but I am having residuals othervise. I am attaching the code, which is a QPM model
dfm.mod (64.9 KB)

4

But how do the trending variables fit together with the rest of the model? Why do only

5

Sorry, If I understand your question correctly, trending variables are defined as AR processes, converging to some steady state values, for example :

[name = '120.Change in real /effective/ exchange rate trend']
dZ_t = rho_4*dZ_t(-1) + (1-rho_4)*EXCH_TREND_SS + E_dZ_t;

Here the steady state of Z_t is EXCH_TREND_SS, which is not zero,
Then I connect the RER with its trend with the following AR(1) way:

[name = '121.Real effective exchange rate trend']
Z_t = Z_t(-1) + dZ_t/4 -EXCH_TREND_SS/4 + E_Z_t;

(Here I also have some issue with steady state, if I omit subtracting EXCH_TREND_SS/4, I am having a residual in this AR(1) equation.)

6

My point is: if you have dZ_t with a non-zero mean, you have to subtract the mean somewhere else in order to have the trend not spill into other variables. As you are doing that, there is an easy solution in the above case. Simply use a detrended version:

[name = '120.Change in real /effective/ exchange rate trend']
dZ_t = rho_4*dZ_t(-1) + E_dZ_t;   
[name = '121.Real effective exchange rate trend']
Z_t = Z_t(-1) + dZ_t/4  + E_Z_t;
7

Then how can I impose that this dZ_t revolves around it’s nonzero steady state?
Also how can I calculate the steady state of S in this case or in the upper case?

8

In my formulation, dZ_t is in deviations from its steady state (which you don’t need to compute) and it has mean 0.