Yes indeed, my ricardian and non ricardian agents have a different level of base consumption. I get your point now. Should I normalize base consumption at my SS to 1 ? So then, I divide my consumption results for every period by the level of SS consumption ?
I am not saying they need to have the same base level. All I am saying is that you need to specify/explain the concrete metric you want to employ. That may be utils or absolute or relative consumption.
That distinction does not matter and you should not use my files. Rather, it’s about the concept. You should know the level of welfare and of consumption in steady state. You also know how welfare changes between two dates. That should allow for backing out the consumption equivalent.
Here you have an example. You have consumption for the two types of households and welfare at SS. Then I have Welfare for the end of period computed from the utility function, and welfare in consumption units computed by a simply rull of three. Is it ok?
One more question: for the computation of welfare, should I include beta or just use the CRRA specification without the parameter beta and the sum ?
The consumption equivalent would be the percentage of steady state consumption to achieve that utility level.
If 30772,65628 steady state consumption would generate a welfare of 1,988632544 as at the end of the period, then you would have a consumption equivalent of (30772.65628-30772.1339)/30772.1339*100= 1.6976e-03 percent.
If you do it in percent, then the beta and the sum do not matter.
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 what’s 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 I’m 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, “The 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 counterparts”. Good practice? Thanks!!