# Welfare analysis in deterministic models

Hi

I wish to compare welfare from two models that have the same steady state and calculate the consumption equivalent (CE) variation.
Both models have deterministic temporary demand and supply shocks that last 10 quarters.

The benchmark model has no other shocks.
The alternative model has deterministic temporary fiscal stimulus shocks that last 10 quarters.
The steady state is the same in both models.

I know how to calculate the consumption equivalent (CE) variation in theory.
How do I calculate the consumption equivalent (CE) variation in Dynare?
Most of the examples in the forum seem to have stochastic shocks when calculating conditional welfare.

Relative to what do you want to compute the CE? Whether the setup is stochastic or deterministic should make no conceptual difference, only one in terms of implementation.

Johannes

I meant to say in my last post that I calculate welfare (W) recursively with the usual expression W = U(c) + beta*W(+1) where utility is log-linear.

I use the simult_ command and can plot the IRF for any variable including welfare.

From the plots some agents are better off in terms of welfare in the alternative model with the 10 quarters of fiscal stimulus (transfers) than in the benchmark model. This happens a few quarters after the last quarter of fiscal stimulus (some agents have highest welfare then). In Dynare, I am assuming that welfare at each quarter is the sum of discounted lifetime utility from that point. Is this interpretation correct?

While that would suffice for general comments, I want to calculate the CE for each agent using the benchmark model relative to the alternative model to have a number - a % of each agents steady consumption. Given log utility this is straightforward to do.

My query was how to do so in Dynare. If I use conditional welfare after the simult_ command the result depends on what information set I condition on. I may be misinterpreting DYNARE here. For example, in looking at the plot of welfare conditional welfare is higher for a certain agent in the alternative model than the benchmark just after the 10 quarters of fiscal stimulus then after quarter 1. So is it reasonable to use the value of welfare from each model in say quarter 11 which would condition on the first 10 quarters?

I replied to your reply on May 1. In that reply I think I answered my own question about calculating conditional welfare after say 10 quarters of a deterministic shock using the simult_ command. I just wanted clarification. Thank you.

Sorry, I somehow missed the original post. I still don’t understand which object you want to consider. `simult_` will return the welfare conditional on the state variables in that particular period. Of course, that object will be time-varying as the conditioning set changes.

Johannes

Thanks. You have implicitly answered my question.

In my model section I calculate welfare (endogenous variable number 88 in DR order) with the usual expression

welfare = log(C) + BETA*welfare(+1);

Later in the .mod file I have

y_=simult_(M_,options_,y0,dr,ex_,iorder);

Finally conditional welfare after 10 observations is

disp(‘Welfare in obs 10 =’); disp(y_(88,10));

It is this value of conditional welfare I want to use in subsequent analysis.

Maurice

No, the output of `simult_` should be in declaration order.