first order approxmation of 'ramsey_policy'

[superztt]

In dynare reference manual, it is said " This command computes the first order approximation of the policy ". Can anyone clarify if it also approximates the objective in the first order? I am hesitating to use 'ramsey_policy' in a stochastic environment to maximize welfare. Cheers!

[jpfeifer]

Please have a look at http://www.monfispol.eu/events/stresa-papers/slides.pdf. Dynare does not do a simple first order approximation.

[superztt]

Thanks for the reference.

I am worried about the missing of the second order moments. In a general mod file that does not look for an optimal policy, a first order approximation of first order condition messes up the welfare analysis, because it could lose the correlation of a variable and the state of the economy, e.g. the price of an equity depends on the correlation of its return and the state.

In 'ramsey_policy', even though the first order approximation involves the second order derivatives of non-authority agents' first order conditions, w.r.t. non-policy variables, according to the slides, it is still the first order approximation of authorities' first order condition (of the lagrangian as in the slides). So it could still miss the policy instruments' correlation with the state of the economy in the policy rules. Am I right?

However, the slides mention the welfare is approximated in the second order, does it refer to the "Approximated value of planner objective function" appearing in the end of the dynare result?

[superztt]

Sorry but I have another two questions.

1. Appears there are two "Approximated value of planner objective function" provided.
- with initial Lagrange multipliers set to 0:
- with initial Lagrange multipliers set to steady state:
I always get the same result actually. Does it mean the lagrange multipliers in the steady state are zero? What is the case there will be nonzero steady state lagrange multipliers?

2. I used the ' ramsey_ policy' and set up lagrangian by myself to solve for the same optimization problem. Unfortunately, the steady state doesn't always coincide. The steady state in the 'ramsey_policy' highly depends on the initial inputs. In other words, the steady state from the two ways will not coincide unless I put in the steady state result of the second way in the 'ramsey policy'. Then, is the optimal policy result from 'ramsey-policy' affected by different inputs of the steady state?

[MichelJuillard]

Thanks for the reference.

I am worried about the missing of the second order moments. In a general mod file that does not look for an optimal policy, a first order approximation of first order condition messes up the welfare analysis, because it could lose the correlation of a variable and the state of the economy, e.g. the price of an equity depends on the correlation of its return and the state.

This is because you would also take a first order approximation of the welfare function

In 'ramsey_policy', even though the first order approximation involves the second order derivatives of non-authority agents' first order conditions, w.r.t. non-policy variables, according to the slides, it is still the first order approximation of authorities' first order condition (of the lagrangian as in the slides). So it could still miss the policy instruments' correlation with the state of the economy in the policy rules. Am I right?

However, the slides mention the welfare is approximated in the second order, does it refer to the "Approximated value of planner objective function" appearing in the end of the dynare result?

In Ramsey policy we compute the first order approximation of the first order conditions of the policy maker optimization problem. This involves the second order derivatives of the objective function of the policy maker. We use a second order approximation to compute the "Approximated value of planner objective function".

[MichelJuillard]

Sorry but I have another two questions.

1. Appears there are two "Approximated value of planner objective function" provided.
- with initial Lagrange multipliers set to 0:
- with initial Lagrange multipliers set to steady state:
I always get the same result actually. Does it mean the lagrange multipliers in the steady state are zero? What is the case there will be nonzero steady state lagrange multipliers?

If the two results are the same, most likely the steady state of the Lagrange multipliers is zero. You can check by displaying oo_.steady_state. M_.endo_names will tell you wich entry corresponds to which variable. Lagrange multipliers are zero qt the steady state in the purely linear quadratic case (linear model with quadratic objective function). In full nonlinear models, they are usually different from zero.

2. I used the ' ramsey_ policy' and set up lagrangian by myself to solve for the same optimization problem. Unfortunately, the steady state doesn't always coincide. The steady state in the 'ramsey_policy' highly depends on the initial inputs. In other words, the steady state from the two ways will not coincide unless I put in the steady state result of the second way in the 'ramsey policy'. Then, is the optimal policy result from 'ramsey-policy' affected by different inputs of the steady state?

It is difficult to answer without having the actual example.

Best

[jpfeifer]

See also the manual clarification at https://github.com/DynareTeam/dynare/pull/872