theoretical mean considering transition dynamics

[lm280299]

Hi everyone,

I hope someone may help me with the following question. I intend to calculate the ex-ante lifetime utility at time t. Before t, the economy has TFP which has a smaller volatility where at t the volatility increases once for all. Thus the agent should have a transition period. I could write the problem in a recursive form, that is, I can express the ex-ante lifetime utility as the value function v=u+beta*v(+1). Basically if I understand the common method of Dynare, I should compute the theoretical mean of v considering transition dynamics.

I don't if I can do it using dynare. Or maybe you have a better idea to measure the ex-ante lifetime utility.

Thank you!

[jpfeifer]

Welfare is a function of the relevant state variables. All you need to know is the value of the state variables when the unexpected change happens. You need to plug in the value of these states into the new decision rules. In your case, the agent will be at the mean given the lower TFP volatility. The states will converge to the mean given the higher volatility. This transition is reflected in the value for welfare using the decision rules given higher TFP volatility, but evaluated at the states reflecting lower volatility.

[lm280299]

Welfare is a function of the relevant state variables. All you need to know is the value of the state variables when the unexpected change happens. You need to plug in the value of these states into the new decision rules. In your case, the agent will be at the mean given the lower TFP volatility. The states will converge to the mean given the higher volatility. This transition is reflected in the value for welfare using the decision rules given higher TFP volatility, but evaluated at the states reflecting lower volatility.

I think I understand what you said. But when I tried to realize the procedures, I found another question: I should input the values at the states indicating the mean with lower volatility at the initval block and should not type "steady". The steady state computation was triggered as well by the command stoch_simul as the guide said. But these steady state values were different from what I computed from the model equations in steady state. I wonder if it means I did wrongly.

Thank you!

[jpfeifer]

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initval

is the wrong place to put these initial conditions. It might have to go into

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histval

depending on what you are trying to do (see the manual). But it might be easier to just use the

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simult_

function to get the desired welfare value given the states