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?

Thank you in advance,

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

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.

It seems to have worked for the previous user. However, you cannot simply replace two equations by a single equation. You also need to reduce the number of variables. It sounds as if the two debt stocks and the two budget constraints were replaced by the balance of payments condition and the aggregate debt stock.

You drop the 2 budget constraints of the agent and you include 1 new equation:balance of payment. By doing this, you drop 2 variables: debt of each agent and you add a new variable that is the sum of the debt of the two agents. You should also combine d_1 and d_2 in the debt elastic interest rate.

Assume that there are agent-specific interest rates that only depend on each agentsâ€™ debt level (i.e., you will have r_1 and r_2). By doing this, interest rates will move in different directions and Euler equations are not collinear anymore. In this case, you need to add an additional equation and variable which will be the interest rate for the remaining agent (you already had one interest rate equation for both agents.

Add an additional â€śstationarity deviceâ€ť as in Schmidtt-Grohe and Uribe (2003). You could add debt adjustment cost for some of the agents. This will generate that Euler equations are not collinear anymore. One of the agent will pay an extra premium. In this case, debt of each agent can be pinned down.

Your choice of any of the alternatives will depend on what your specific model is trying to say.
I hope this can help,

Thank you very much for your suggestions!!!. I will try to adapt them to my model. I have slightly different setup as there is one household who does the investment (home and aborad) and two sectors (manufacturing and services) who trade.