I post this message because there is something that I do not fully understand in the welfare decomposition. I am working with a model where I compute the conditional welfare as : W=W^{ss} +1/2\times Var^{W} which is as in SGU(2004-2007) and then I compute the consumption equivalent in the cycle as being the difference between the welfare under a given policy regime minus the welfare in the steady-state, in the same spirit than Lucas(1987). But in Kim and Kim (2018) they further do a decomposition of welfare variation as being the sum of the mean and the variance effect but in the SGU representation, fluctuations in welfare can only be due to variance effect by construction no ? Can someone explain me what is the difference between the two approaches ? I think that in Kim and Kim they do not rely on the same definition of conditional welfare but I am not completely sure. Thanks in advance for your reply.
Best,
Hugo
If I understand that paper correctly, in their conditional welfare analysis the steady states across regimes will be different, causing differences in the W^{ss}.
But in their paper they study the welfare decomposition when they change “eta” which is a parameter of the fiscal rule that does not change the steady-state no ?
In the closed economy, active tax policy can be welfare improving because governments should finance fiscal spending (which is positive and exogenously given) by collecting distortionary taxes. Since the steady-state tax rates are positive, taxes would introduce distortions in the static and intertemporal optimality conditions. Therefore, contingent tax policies can improve welfare by redistributing such distortions in a better way. We first calculate the level of welfare when tax rates are fixed at the steady-state level and then measure potential welfare gains when governments adopt active tax policy relative to the benchmark fixed-tax case.
That sounds like the tax rate in steady state changes.
In fact but there is something I do not understand because my question is about table 2 at page 361 where it seems that they set a tax rate and look at how different values of “eta” affect the welfare gains that they then decompose into the mean and the variance effect but conditional on the tax rate that they set no ? I do not see there that the steady-state changes. On top of that they define the mean effect as changes in the conditional mean of the variables, this is different from steady-state effect no ?
