Unconditional versus conditional Welfare measure

Dear all,
I have a question regarding the proper way of calculating the value of both the unconditional and conditional (upon starting from the steady state) welfare measure. From what I see after browsing similar questions here in the forum, in Dynare the unconditional welfare corresponds to the unconditional ergodic mean of the welfare variable:

Welfare_pos=strmatch(‘Welfare’,M_.endo_names,‘exact’);
Welfare_uncon=oo_.mean(Welfare_pos);

By contrast, the conditional welfare criterion (upon starting in the steady state) is given by the constant in the policy and transition functions output that Dynare produces. Guess its interpretation is…the conditional ergodic mean which in a 2nd order approximation is different from the steady state. The way I compute is:

Welfare_pos=strmatch(‘Welfare’,M_.endo_names,‘exact’);
Welfare_con = oo_.dr.ys(Welfare_pos)+0.5*oo_.dr.ghs2(oo_.dr.inv_order_var(Welfare_pos));

Is that right? I am asking since I obtain very weird values for the conditional welfare both in sign and in values as they are very different from the unconditional welfare measure.

Best,
Peter

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Yes, that is correct. If you are in the steady state, you can use the steady state plus the uncertainty correction. You can cross check this with

initial_condition_states = repmat(oo_.dr.ys,1,M_.maximum_lag); %get steady state as initial condition
shock_matrix = zeros(1,M_.exo_nbr); %create shock matrix with number of time periods in rows
y_sim = simult_(initial_condition_states,oo_.dr,shock_matrix,options_.order); %simulate one period to get value
Welfare_con_2=y_sim(Welfare_pos,2)*100; %read out gap

as in

The interpretation is that this is the welfare conditional on being in the steady state, but factoring in that the model is stochastic, i.e. that shocks in the future may happen.

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Perfect match, many thanks Johannes.

But Professor Johannes, isn’t what you just said the same as Valerio said in:

Back there you said this is a wrong way of computing conditional welfare as we can see in:

I am not sure I understand your post. For conditional welfare, you take the first element of the simulation without shocks, not the last one of a long simulation.

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Thank you for the response! That was indeed my question! :slight_smile:

Hi Professor,

Is the unconditional welfare the risky steady state of welfare?

Best,
Yunpeng

Hi @dypisgood In my humble opinion, no.

Deterministic Steady State: when we want to compute the conditional welfare, usually we start/perturb the economy from this type of steady state. At the steady state, there are no shocks.

Risky Steady State: despite no shocks, the agent observes the distribution of the shocks that may hit the economy in future, e.g. standard deviation \sigma. In this context, we simulate long sequences of endogenous variables at a higher order to see they will converge to the risky steady state or the stochastic steady state.

Ergodic/unconditional mean: We get this value by simulating the economy with shocks after a long-run period to compute the unconditional welfare.

Yes, unconditional welfare is the average welfare with shocks.