Two-identical-sector model with CRS - collinearity issue

General DSGE Modeling
1

Hi,

I tried a model with two identical (!) sectors (i.e., not consumption and investment), just two production functions for two identical goods (same price). The file is attached (CRS_NoLand.mod). I get the message that a set of equations is collinear.

I suspect this is because in such model it is not determined how big sector 1 and sector 2 is (it can be anything), but I am not sure if this line of thinking is correct. To look into this further, I made a version of the model with land and hence decreasing returns to scale for capital-and-labour-part of the production function (attached, DRS_WithLand.mod). Now the collinearity message is gone, and I think this is because sectors now have to be of equal size in order for the equilibrium to be symmetric.

CRS_NoLand.mod (1.5 KB)
DRS_WithLand.mod (1.6 KB)

Does this make sense? Many thanks in advance!

2

Hard to tell, but it sounds reasonable.

3

Thank you very much! Well, then it is two of us who believe this is reasonable. I hope it does not mean we have converged to the same fallacy :slight_smile: If I find out more about this, I’ll post it here.