Hi, I am currently working on my Master thesis on climate policy analysis and I am trying to solve a dynamic deterministic general equilibrium model. This model is a classical Cass Koopman Ramsey model with a geometric growth of TFP and in which I added a durable goods producers sector. The representative household can choose either to consume this durable (in a CES) or to rent it to firms. (If needed I can give more details about the formal model equations.) I would like to ask, how dynare would numerically solve this ?
I think that it needs a starting condition for stocks variables and a terminal condition, which would be the steady state of my optimality equations system, and then it finds the root (Newton algorithm) of a systeme of N equations with N unknowns.
If this is the case and if my understanding is correct, I first need to rewrite my system as a function of deflated variables only which have a steady state. But which variables should I deflate ? I read in a some papers that in such model, labor is constant at steady state, but are there other variables behaving like this ?
Many thanks in advance for your help which would greatly help me in my research.
Thanks a lot for your answer, that makes me much more confident. I could detrend my model assuming a steady would exist but I assumed that at this steady state the prices of my 2 goods and labor supply/demand are constant. Capital, consumption and output are constant once they are deflated by labor productivity. I think it is a classic hypothesis am I still right ?
Yes, that is correct. It is well-known that there are particular preferences that are consistent with a BGP. They ascertain that labor supply is constant. Typically, the only tricky part in detrending is the Lagrange multiplier on the budget constraint. See
I still have two last questions : 1) one about the Lagrange multiplier and 2) another about steady states in bigger models with both exogenous productivity growth and learning by doing elements.
I could rewrite the household’s program as a function of stationnary variables. So, my budget constraint is slightly modified, a (1 + g) appears in front of the capital (from last period) returns. Is it still the case that the lagrange multiplier has a trend ? Since my budget constraint is divided by the productivity now, it does not have the same interpretation as before right ? Here is my budget constraint in level :
-The factor added to account for this, is the aggregate capital. This is an externality, it is taken as given by firms.
-So I understand that, if I add such elements, I also need to deflate this aggregate capital by the exogenous productivity to stationnarize the model, right ?