# Unit root -SOE model - colinear equations

Hello everyone,

I am working with a small open economy model with 2 sectors and 2 workers. The only difference between workers is the intensity with which each sector employs them; i.e: one sector is intensive in worker type 1, while the other sector is intensive in worker type 2. Workers consume, supply labor and save in foreign bonds. (I attached here a pdf file with a description of the model and main equations )

Problem: When I try to solve the model I get a unit root. In particular, there seems to be a â€ścollinear relationshipâ€ť between the Euler equations of both agents (equations 1 and 2). I attach here a matlab code â€śrun.mâ€ť that solves for the steady state and then runs the dynare code â€ścode.modâ€ť.

I know that this is a common problem in SOE models. Usually, to break that non-stationarity, a debt elastic-interest rate is introduced (as in Schmidtt Grohe-Uribe, 2003). I did that, of course, but the problem is still there. I have read several posts on the forum talking about this topic but I still canâ€™t figure out what is not working.

Do you have some idea on how I should tackle the issue?

pd: If I solve the model assuming that one of the agent is HtM, then the non-stationary problem dissapears.

model___Dynare_forum.pdf (157.4 KB)
run.m (4.1 KB)

code.mod (3.9 KB)

may contain the answer. Due to the permanent income hypothesis, there may be a (expected) unit.

Thank you very much Professor,
I will check the post and see if I can find the answer there.

I think I found the solution. As the model is written, the amount of debt that each agent has individually canâ€™t be determined. However, it is possible to determine the amount of debt of the economy as a whole (sum of debt of household 1 and 2). Then, both agentsâ€™ budget constraints should be replaced by the aggregate balance of payment equation.

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