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

General DSGE Modeling
1

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)

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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)

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I would really appreciate any help.

4

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

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