Problems about welfare analysis

I am currently conducting a deterministic simulation that traces the transition from a non-steady state to the steady state. My goal is to compare the transition paths under different policy scenarios starting from the same initial condition, using consumption equivalent welfare as the evaluation metric. However, I am confused because, as far as I understand, welfare analysis typically requires a second-order approximation, while deterministic simulations are usually based on first-order solutions. How can this issue be resolved?

What exactly are you trying to do? Conditional welfare in a stochastic setup? Or welfare in a perfect foresight context?

I am trying to do welfare analysis in a perfect foresight context.

Then you don’t need to worry about approximation orders. The model will be solved fully nonlinearly.

Thank you very much for your response. Could you please provide me with an example of welfare analysis under deterministic simulation?

An example would be

Thanks! It helps me a lot.