# Measures of welfare gains/losses

Good evening everyone,

I wanted to know how one computes the welfare gains and losses between two dates in a perfect foresight simulation. Should I compute the difference between the two utilities from the two dates ?

Thanks!

best regards

1. Are you talking about welfare or utility/felicity?
2. Yes, you can define the object in the model and compare the points in time. The only challenge usually is the units, i.e. whether you want steady state consumption equivalents.
1. I am talking about welfare;
2. I only want to know the % change of welfare from one date to another, and if my ricardian household gains more utility than my non-ricardian household. Does unit matter ?

Thank you @jpfeifer

Best regards

Yes, units matter. Depending on your concept of utility, it’s for example not comparable across agents. So how do you measure whether a particular household gains more utility if it is measured in different things?

Thank you @jpfeifer

How do you change units manually to make the utility comparable ? I have al the results for my simulations, so I was wondering if I could change units by hand.

Best regards

or some other variant of it where you compare units of the consumption good required to make utility the same.

That does not matter to me. I just want to know which agent gains the most from the shock. Dynamics only matter to me, not the level.

How do I perform that with SS consumption equivalent ? Is there a formula ?

Thank you @jpfeifer

Again, the problem is how you define most.
Take two agents with log utility. One starting with 0.01 consumption, the other one with 0.1. Both gain the same additional units of consumption 0.001. But their gain in utility is very different:

``````log(0.01)=   -4.6052
log(0.011)=   -4.5099
log(0.1)=   -2.3026
log(0.101)=   -2.2926
``````
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I have a simple CRRA utility function with only consumption in it @jpfeifer

But you are comparing different agents with potentially different base consumption levels. In my example above, both gain the same units of consumption, a very different percentage of their initial base consumption and very different levels of utility. You need to decide what you want to compare. Everything is easy to compute in your model.

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 ?

Thanks @jpfeifer

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.

I’m not sure what to answer to that. I would go for relative consumption as I’m comparing between two dates the gains @jpfeifer

That sounds reasonable.

So now, how do I perform that ? Just by comparing the gain of relative consumption between two dates for my two agents ? @jpfeifer

It’s more complicated as we are talking about welfare, so the path of utility matters. Usually, you do something like

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Thank you @jpfeifer

I find it quite difficult to replicate your files as I do not compare two policies, but the gain of welfare between two dates after a shock.

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.

Thanks @jpfeifer . I think I got it.

SS End of period End of period
Cr 30772,1339
Cnr 27210,7542
Wr 1,988598784 1,988632544 30772,65628 consumpt eq
Wnr 1,987875615 1,987883907 27210,86772 consumpt eq

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 ?

Thanls

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.