I am trying to find the values of a set of parameters that maximize an objective function, i.e total welfare, given a set of constraints. Hence, I have used the ramsey_model command followed by the steady command. To find the steady state I have done a numerical guess for each variable in Initval.
My problem is that when I change the guesses in Initval I obtain different values for the steady states. Probably this is due to the fact that there are multiple-infinite steady states since the objective function and some constraints are nonlinar. Indeed, the check commad tells me that one of the eigenvalues is close to one.
Is there a way to get the steady state/the values of the parameters what make the value of the objective function as big as possible?
Attached there is my .mod file.
I thank you for your time,
Decentralized.mod (3.2 KB)
Does the model without Ramsey also have a unit root?
Dear Dr. Pfeifer, thanks to answer me. But I am not sure to understand the question.
The idea of my model is that there is a planner that chooses the value of two variables, g (public expenditure) and tau (tax rate), to maximize social welfare subject to the optimal behavior of the agents and of a representative firm. If I set the Lagrangian and I compute manually the FOCs for g and tau, these two FOCs contain the lagrangain multipliers of all the constraints. Consequently, if I set a model with these two FOCs, the optimal behaviors of agents and firm, the feasibility constraint and government budget constraint, I have more endogenous variables than equations.
Hence, I have tried to avoid these problem using the ramsey_model command for computing the FOCs for g and tau, followed by the command steady .
That sounds like your model is incorrect. How can you set g and \tau optimally when the government budget constraint needs to hold? Doesn’t a level of government spending tell you the amount of revenues to be raised?