I have some questions about Ramsey optimal policy.
My model is a standard CEE model (without habit formation consumption). It works fine if I put Taylor rule as the monetary policy rule. But there's a problem when I try to get the results under Ramsey optimal policy. I log-linearized the equilibrium equations, including the planner's objective, up to first-order. The resulting planner's objective is a linear function of consumption expenditure and labour hours. When I try to run the code, Dynare returns the following error message:
Some elements of Newton direction isn’t finite. Jacobian maybe singular or there is a problem with initial values.
I found that if I change the planner's objective to a quadratic function, or Woodford's welfare loss function, the code works fine.
I read from papers about Linear-Quadratic approximation (e.g. Benigno and Woodford 2004) that in a problem like this, the objective has to be quadratic and the constraints need to be linear. Does it mean that I can't have a linear objective if I have a linear model? If I try to approximate the objective up to second-order, would that solve the problem?
Any help would be much appreciated!