Unit root -SOE model - colinear equations

[emilio]

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 “collinear relationship” between the Euler equations of both agents (equations 1 and 2). I attach here a matlab code “run.m” that solves for the steady state and then runs the dynare code “code.mod”.

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 can’t figure out what is not working.

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

Thank you in advance,

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)

[jpfeifer]

Colinearity in a two-households-model due to similar euler equations

No, I am saying that there might be something like the permanent income hypothesis at work. Any shock that moves the debt position will move it permanently and there is no tendency to return to the old level. That is a common thing happening under perfect foresight. Things usually change under stochastics. For example, the unit root in small open economy models vanishes when agents take future shocks into account. The same happens in consumption Euler equations due to Jensen’s Inequality.

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

[emilio]

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

[emilio]

@emilio

Problem: When I try to solve the model I get a unit root. In particular, there seems to be a “collinear relationship” between the Euler equations of both agents (equations 1 and 2). I attach here a matlab code “run.m” that solves for the steady state and then runs the dynare code “code.mod”.

I think I found the solution. As the model is written, the amount of debt that each agent has individually can’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 agents’ budget constraints should be replaced by the aggregate balance of payment equation.