# Welfare Consumption Equivalent

Hello,

I have a model where I compute a series of policy shocks, two different combinations. The SS consumption and labor of the two economies are the same, so the SS welfare is the same.

I want to compute the consumption equivalent to rank the policies. The benchmark would be the SS. (It’s a CES utility function, not consumption log as in this formula)

I’m not sure about the difference in a setting like this between conditional and unconditional welfare.

Thanks

What do you mean with

? Do agents in the model know the sequence of shocks? Or are they surprised in each period?

In both policies there’s an unexpected shock at the beginning and the CB announces different policies (sequence of shocks) that same period. I’m interested in ranking the policies under a welfare consumption equivalent approach. Thank you!

That sounds like a perfect foresight exercise where you can simply define welfare recursively in the model block to retrieve the conditional welfare value in the first period. That value can then be use to compute the consumption equivalent.

Thank you so much. You are correct. It’s a perfect foresight exercise. I already defined the recursive welfare in the model block. After conducting the exercises I have a vector of welfare. Should I take the differences (from example between this welfare vector and the SS) across the whole sample, discounting it, or is it just the difference in the first period?

It’s just the difference in the first simulation period. Be careful not to include the starting value used for initializing the lags.

Thank you so much, Johannes. One last question: now I added a third policy to the comparison: the Central Bank announced a looser policy say in period t=5 using the PF with surprises. For the Welfare ranking, should I proceed the same way?

What are you trying to measure in this case? Before the shock happens, welfare should be at the steady state level as nothing happens during the initial phase.

Johannes,

Sorry, let me be clear about the whole experinment. I want to to a welfare ranking across 5 experiments in a PF exercise.

1. Negative K Quality Shock, No policy
2. Negative K Quality Shock, and policy A at the initial period
3. Negative K Quality Shock, and policy B at the initial period
4. Negative K Quality Shock, and policy A announced at the initial period. At t=5, policy B is announced and implemented
Negative K Quality Shock, and policy B announced at the initial period. At t=5, policy A is announced and implemented.

So for scenarios 1,2,3 I should look at the recursive welfare initial period, as you mentioned. Does this still apply for scenarios 4 and 5?

Thank you so much!

Yes, for the first third you can just look at recursive welfare in the first period. The final two scenarios are tricky, because the announcement in the first period does not coincide with what happens at t=5. Thus, there is no encompassing measure you could compute at time 0.

Thank you so much. So, is it not possible to compare them according to welfare, right? The first three are comparable in a straightforward way. Maybe the latter two can be compared at the t=5 period, right?

Yes, that is what I would do.