# Two region model when one representative firm has establishments in both regions

I have a two-region model where a representative firm has establishments in both regions. The firm is subject to a borrowing constraint which limits its borrowing to a fraction of its EBITDA. The firm maximizes its dividend, d and chooses n1,n2,k1,k2 and borrowing b (=b1+b2). There is a tax advantage on debt and thus borrowing exists in the model and the firm borrows up to its borrowing constraint. The firm accumulates capital in the model.

Both regions have a representative HH who chooses c_i, n_i and b_i and earn wages w_i by supplying labor to the firm. Households in both regions own equal shares of the firm (1/2 each) and thus get half of the firm’s dividend in each period.

To pay for the firm’s tax advantage, govt taxes both households equally in a lump-sum way.

This was to give a background of the model. I allow for firm to have different productivities in two regions and I want to see reallocation of resources by the firm in response to productivity shocks. When I run my model, I find that Euler equations of the two households are collinear. What is the reason for this? Should I get this?

My model runs a gives me IRFs in response to shocks but when I do model diagnostics, I get the following problem:

MODEL_DIAGNOSTICS: The Jacobian of the static model is singular
MODEL_DIAGNOSTICS: there is 1 colinear relationships between the variables and the equations
Colinear variables:
c1
c2
b1
b2
Colinear equations
5 6

MODEL_DIAGNOSTICS: The singularity seems to be (partly) caused by the presence of a unit root
as the absolute value of one eigenvalue is in the range of ±1e-6 to 1. If the model is actually supposed to feature unit root behavior, such a warning is expected, but you should nevertheless check whether there is an additional singularity problem. The presence of a singularity problem typically indicates that there is one redundant equation entered in the model block, while another non-redundant equation
is missing. The problem often derives from Walras Law.

Please find the mod file attached. Any help would be highly appreciated.

new3.mod (2.0 KB)

Please find the mod file with comments so that equations are clear. And also firm discount profits by the MU of HH1 (the problem still persists if I do it by MU of HH2 or a weighted avg of HH1 and HH2). In the updated mod file, the collinearity is between equation 12 and 13. The error is same as mentioned before. Thanks a lot in advance.

new3.mod (2.7 KB)

I would really appreciate any help.

Hi, this is not an error, but rather a warning. It comes from your model having a unit root. That explains why the effects are permanent. Maybe you have the same issue as in

Thanks Professor! It works after adding bond adjustment cost in HH budget constraint as in Schmitt-Grohe and Uribe (2003).