collinearity/Bk problem

Stochastic simulations
1

Hello everyone,

I try to run the attached open-economy model that I have build, before that, my model was in closed economy and it worked well. I have introduced the simplest way to move from a closed to an open economy. I just have added the features necessary for imports-exports (no foreign debt). However, when I try to run the model, the BK conditions are not satisfied due to a collinearity problem. As I have added only 6 equations between the closed and the open model I do not see where is the problem because in my view, all the equations are necessary…
I would really appreciate if someone can help me with this.

Thanks in advance :slight_smile:

Hugo

SimpleNk5opennew_steadystate.m (2.8 KB)

SimpleNk5opennew.mod (5.3 KB)

2

The problem is not the collinearity (yet). You model features explosive behavior. Most probably it’s an issue with the fiscal rules.

3

Dear Mr Pfeifer,

Thanks for you reply, in fact I changed my fiscal rule by setting zeta=0 and increasing the fiscale brake lambda_b from 0.01 to 0.05, now the model runs, BK are satisfied, but the model diagnostic still tells me that I have collinearity, also when I look at my IRFs some variables do not go back to their steady-state, for instance, after a shock on public expenditures, consumption of home good and consumption or foreign goods do not go back to their steady-states. My model was correct in closed-economy do you think one of my equations from the open economy framework is wrong or redundant which could cause the issue just described ?
Thanks in advance for your answer :slight_smile:

4

I don’t think this is uncommon. See e.g.

5

But in Schmitt-Grohe, the problem is linked to foreign debt if I’m correct but in my model , I just have exports and imports, no foreign debt, that’s why it looks weird.
Don’t you think it is linked to one of my open economy equations ?
Again, thanks for you reply.

6

Use irf=2000 to see which variables are affected. That often helps. When you say

are you saying that your model features balanced trade, i.e. imports always equal exports? Because without a net asset position to draw from. how would you finance trade surpluses and deficits?

7

Yes exactly, I just have a BOP condition stating that X=eM where e is the real exchange rate, imports M are just equal to home consumption of foreign goods (Cf). That’s very simple and I do not see why it may be not correct…

8

But where is the unit root in your model, i.e. which variables are affected.

9

Dynare tells me that it is linked to equation 8, 11, 29,30. And it tells me that 21 variables of my model are collinear. Is it your question ?

10

No, the question is which variables display NaN theoretical moments and do not return to steady state in the IRFs.

11

When I look at theoretical moments (mean, variance) , no variable display NaN. However when I look at the IRF , a lot of variables do not go back to their steady-state but in my view it is induced by the lack of convergence of the variables linked to the open-economy framework ( exports, imports, consumption of home good and consumption of foreign goods).

12

Could you please provide the most recent file.

13

Yes sure, here are the most recent files.
Thank you very much.

model1.mod (5.3 KB)
model1_steadystate.m (2.8 KB)

14

From what I can see

  e=(pi_f/pi_h)*e(-1);
  X=e*M;

implies a unit root for e, which will affect imports and exports.

15

Thanks Mr Pfeifer, but how can I solve this issue ?

16

If that is the correct equation, then there is nothing to fix. It’s just the way the model works. Otherwise, fix the model.

17

Dear Mr Pfeifer,

Thanks for your help, it helps me a lot.

Have a good day.

Best,

Hugo