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)