Conditional welfare evaluation confusion

[mch]

Dear Dynare users,

My aim is to compute conditional welfare at time 0 using Dynare, where at time 0 all variables are at their steady-state values as in Schmitt-Grohe and Uribe's (2007) paper on simple and implementable rules. If I understand correctly, Dynare simulations will start at the steady-state as long as I provide the correct initial values.

However, my confusion is that many users of the forum say that they calculate conditional welfare using the mean of

Utility = Utility_t + beta*Utility(+1)

where Utility_t is the period utility function, eg c^(1-sigma)/(1-sigma)

But taking the mean implies averaging over Utility for different initial conditions (ie those for period 0 up to T (the simulation length)), so this is not conditional utility at all!

It seems to me that the correct approach is to look at the first simulated value (ie period 0) of the Utility series. Is that right?

If I run many simulations, would it make sense to average over the values of Utility in period 0 from each simulation, as in this case the initial conditions are the same each time but the random seed will vary?

Thanks,
Michael

[MichelJuillard]

You are correct in your approach to conditional welfare. Mean utility or mean welfare as nothing to do with conditional welfare.

Your formula however doesn't make sense. You must mean the definition of welfare copmuted as

Code: Select all

Welfare_t = Utility_t + beta E_t Welfare_{t+1}

Welfare is conditional on the value of state variables (including lagged Lagrange multipliers) in the previous period.

If you average Welfare in the first period of several simulations with different seeds, you will average over the shocks occuring in first period (what you call Period 0)

Best

Michel

[mch]

OK Michel - many thanks!
Cheers,
Michael

[ahnulxy]

You are correct in your approach to conditional welfare. Mean utility or mean welfare as nothing to do with conditional welfare.

Your formula however doesn't make sense. You must mean the definition of welfare copmuted as

Code: Select all

Welfare_t = Utility_t + beta E_t Welfare_{t+1}

Welfare is conditional on the value of state variables (including lagged Lagrange multipliers) in the previous period.

If you average Welfare in the first period of several simulations with different seeds, you will average over the shocks occuring in first period (what you call Period 0)

Best

Michel

Very good explanation! This is exactly what I am confusing! Thanks very much!