A DSGE model with two different producer

Hello everyone!
Recently I have tried to construct a DSGE model wich separate the intermediate producer into two different kinds, one producer has higher capital elasticity of output, and the other one has lower capital elasticity of output, and the private consumption is compounded by the CES form of these two final products, the labor and private investment also follow this CES form, the two final production have different prices and factor costs(wage and capital marginal return).
But when I simulate this model, the varibles are hard to converge to zero. Someone tell me since the capital elasticity of output are different in two producers, so the labor and capital can flow between this two departments, so this model don’t have steady-state equilibrium solution. Is this explanation correct? If not, what may cause this result, and can someone suggest some paper whose DSGE model with two different producers?
Also someone recommend a paper which study a model with two producers, and conclusion in this paper is this kind of model can’t have steady-state solution, I remember vaguely the name of this paper is “Beyond *** gross”, I want to read this paper, but I can’t find this paper, if you know this paper, could tell me the correct name of this paper?
Your help is very important for me, looking forward to your reply! Thank you!

Which convergence are you talking about? Also, did you check out Two-Sector Model with Adjustment Costs ?

Hi Sherry,

which technology do you assume in the two sectors? Cobb-Douglas or some different returns to scale in each sector?
I think that as long as you have two different capital elasticities (and thus two different capital-labor shares in your model), you should be able to identify capital, labor, wages and the interest rates in the two sectors, and later back out all the other variables in your model.
If you are unsure whether there is a unique steady state identified by your model equations, start with writing down all model equations (all FOCs, law of motions and market clearing conditions) and all variables you need to identify. This helps you to see if you have enough equations to solve the system. Otherwise, it is difficult to see if you can find a unique steady state or not. Proceeding like this, you are sure that the issue you face in the IRFs is not caused by your steady state result. And if there happens that there is no uniquely defined steady state in your model, you will know that you have to work on a solution for this problem, before jumping to IRFs.

Good luck! :slight_smile: