Gap-Trend model

Estimation ML/Bayesian estimation
1

Hello Dynare folks,

I am estimating and Gap-Trend model where unit root exist in some equations as in the definition of the quarterly (Q on Q) inflation, DL_P = 4(P-P(-1)) where P is the log of CPI.

Given the model is linear, I tried to solve for Steady state values as advised in previous posts and use -steady_state_model- however although DL_P (annualized quarterly inflation) steady state is known in the SS (which is the inflation target) , then how to get/obtain price level of steady state where, again, DL_P = 4(P-P(-1)) . In steady state P=P(-1) so how it is possible to get the steady value of unit root variable P=log(CPI) ?

Thx a lot

2

The steady state of a unit root variable is not uniquely defined. Typically, in estimation you can simply put any value for that variable, it should not matter with the diffuse_filter.

3

Thank you for the reply.I have mis-interpret the problem. I should have said that I am after simulating the model and get the IRFs :slight_smile:. Namely, should I impose any arbitrary value for P in DL_P = 4(P-P(-1)) given P is a unit root process and if DL_P is constant (inflation target value) then P becomes unit root with drift ?

4

Yes, for simulations you can impose any value you like. If you want to have a drift, you need a linear model and use the nocheck option of steady. See

5

Thank you alot. May I ask something trivial ?

In the example you provided in the second link:

mmu= mmu(-1) + bbeta(-1) + e_lev/1000 ;

Bbeta(-1) goes to bbeta_const= 0.0075, then mmu shouldnt be regarded as unit root with a drift ?

I am a bit confused since as I know that when a drift exists then there is not solution at all. In this case (as in the equation above where mmu is a unit root with drift) then imposing arbitrary numbers still work ?

6

That is the point of the nocheck option. You override trying to compute the steady state because it does not exist. But in a linear model, the steady state values will not matter for the slope of the policy function, so it’s fine.

7

Thank you alot :slight_smile: