But is my computation of 30772,65628 is correct in the first place ? The welfare at the end of period, according to the CRRA utility, is 1,988632544. To get welfare in consumption equivalent I did the following calculation: (1,988632544*30772,1339)/1,988598784 = 30772,65628
If the computation is okay, I have, as you computed, a welfare gain of 1,6976e-03 % in the end of period compared to the SS. I find this value rather low as the household consumed 30772,1339 at the SS and at the end of period it consumed 30955,1884. So there is a gain of more than 200 in terms of consumption
How do I know which household gains the most in terms of welfare? To achieve the welfare at the end of period, the ricardian has a SS consumption equivalent of 0,0017% and the non ricardian 0,0004%. Does that mean that the ricardian gains more in terms of welfare ?
Usually, this is wrong. You seem to be comparing utilities directly instead of the consumption levels giving rise to this utility. In W_{model}=W((1-\lambda)c_{ss}) you want to solve for lambda
Welfare gains in most models are tiny. See e.g. Lucas (2003) presidential address to the AEA
Welfare usually has arbitrary units as discussed above. If the metric you use is the share of steady state consumption, then the answer would be yes.
So whatâs wrong with my computation ? I thought I had to express the utility of the end of period in consumption SS equivalent.
The utility at SS corresponds to a value of 1,988598784, consumption at SS to a value of 30772,1339, and utility at the end of period to 1,988632544. In my point of view, expressing the end of period utility in terms of SS consumption give rise to this calculation: (1,988632544*30772,1339)/1,988598784 = 30772,65628
And then comparing the two consumption SS equivalent gives me the gain of welfare between two periods: (30772.65628-30772.1339)/30772.1339*100= 1.6976e-03 percent.
Welfare aka lifetime utility is a more complicated object as the time path of consumption obviously matters. Risk-averse agents prefer smooth consumption paths. For that reason, you cannot use the period utility for any comparison.
Oh okay. Well I think Iâm just going to talk about the increase of consumption I have and not talk about welfare as the computation seems to be tricky.
and the fact that both types of agents receive the same wage does not mean that Cr = Cnr in steady-state?
Some papers also impose Cr=Cnr with statements like, âThe steady-state consumption and hours worked are assumed to be the same among both types of households so that, for a steady-state share of liquidity-constrained households of one-half, they are equal to their aggregate counterpartsâ. Good practice? Thanks!!
