Can I compute the diference between welfare and welfare steady state?

Dear professor,
I am computing the optimal monetary policy based on welfare maximization. I have two policy regimes. welfare_I and welfare_II denote the welfare of two models. And welfare_steady_I and welfare_steady_II denote the steady-state welfare values of two models.
I define
Dwelfare_I =welfare_I - welfare_steady_I;
Dwelfare_II =welfare_II - welfare_steady_II;

 Then I define

delta = (Dwelfare_II - Dwelfare_I) / Dwelfare_I;

My problem is, can ‘delta’ measure the welfare improvement effect of regime II over regime I?


You can, but the number does not have a good interpretation. That is why people measure welfare improvements in consumption-equivalent units.

1 Like

Many Thanks!!! Why did you withdrawn the reply? Does it wrong?

I would like to connect this topic with the one that I posted one year ago, and then ask some naive questions.

If “welfare_steady_I”\neq “welfare_steady_II”, how to compute the consumption equivalence?


Since steady states under two alternative regimes do not coincide, it seems that the unconditional welfare is more rational here?

Suppose we have a separable and additive CRRA utility form. Does it mean:
W^a_0-W^b_0 = \mathbb{E}_0 \displaystyle\sum_{t=0}^{\infty} \beta^t\left[ U\left(\left(1+\Delta^{unc}\right)C^b_{t}, N^a_{t}\right) - U\left(C^b_{t}, N^b_{t}\right) \right]

= \mathbb{E}_0 \displaystyle \sum_{t=0}^{\infty} \beta^t \left[ \frac{ \left(\left(1+\Delta^{unc}\right)C^{b}_{t}\right)^{1-\sigma} -{C^{b}_{t}}^{1-\sigma} }{1-\sigma} - \frac{{N^a_t}^{1-\sigma}-{N^b_t}^{1-\sigma}}{1-\sigma}\right].

\Rightarrow \Delta^{unc} = \left\{\left[ \left( W^a_0-W^b_0 \right)\left(1-\sigma\right)\left(1-\beta\right) +\left( {N^a}^{1-\sigma}-{N^b}^{1-\sigma} \right)\right] {C^b}^{\sigma-1}+1\right\}^{\frac{1}{1-\sigma}}-1

But, I never saw this sort of expression, containing labor, in the literature. It looks ugly…

How did you eliminate the expected value if you are not in the steady state?