# Measures of welfare gains/losses **URL:** \ **Category:** Macroeconomic Model Data Base\ **Created:** [3 February 2021 16:49 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425 "2021-02-03T16:49:51Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![dacorb](https://forum.dynare.org/letter_avatar_proxy/v4/letter/d/bb73d2/32.png) [@dacorb](https://forum.dynare.org/u/dacorb)\ **Post date:** [3 February 2021 16:49 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/1 "2021-02-03T16:49:51Z")
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 ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [3 February 2021 19:50 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/2 "2021-02-03T19:50:43Z")
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. ---
**Author:** ![dacorb](https://forum.dynare.org/letter_avatar_proxy/v4/letter/d/bb73d2/32.png) [@dacorb](https://forum.dynare.org/u/dacorb)\ **Post date:** [3 February 2021 21:18 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/3 "2021-02-03T21:18:03Z")
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 ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [5 February 2021 09:00 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/4 "2021-02-05T09:00:55Z")
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? ---
**Author:** ![dacorb](https://forum.dynare.org/letter_avatar_proxy/v4/letter/d/bb73d2/32.png) [@dacorb](https://forum.dynare.org/u/dacorb)\ **Post date:** [5 February 2021 09:03 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/5 "2021-02-05T09:03:28Z")
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 ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [5 February 2021 09:04 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/6 "2021-02-05T09:04:40Z")
That’s why I asked about > [@jpfeifer](#): > > steady state consumption equivalents or some other variant of it where you compare units of the consumption good required to make utility the same. ---
**Author:** ![dacorb](https://forum.dynare.org/letter_avatar_proxy/v4/letter/d/bb73d2/32.png) [@dacorb](https://forum.dynare.org/u/dacorb)\ **Post date:** [5 February 2021 09:07 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/7 "2021-02-05T09:07:27Z")
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 ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [5 February 2021 09:11 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/8 "2021-02-05T09:11:50Z")
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: ```auto log(0.01)= -4.6052 log(0.011)= -4.5099 log(0.1)= -2.3026 log(0.101)= -2.2926 ``` ---
**Author:** ![dacorb](https://forum.dynare.org/letter_avatar_proxy/v4/letter/d/bb73d2/32.png) [@dacorb](https://forum.dynare.org/u/dacorb)\ **Post date:** [5 February 2021 09:13 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/9 "2021-02-05T09:13:44Z")
I have a simple CRRA utility function with only consumption in it @jpfeifer ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [5 February 2021 09:15 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/10 "2021-02-05T09:15:42Z")
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. ---
**Author:** ![dacorb](https://forum.dynare.org/letter_avatar_proxy/v4/letter/d/bb73d2/32.png) [@dacorb](https://forum.dynare.org/u/dacorb)\ **Post date:** [5 February 2021 09:18 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/11 "2021-02-05T09:18:00Z")
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 ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [5 February 2021 09:20 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/12 "2021-02-05T09:20:53Z")
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. ---
**Author:** ![dacorb](https://forum.dynare.org/letter_avatar_proxy/v4/letter/d/bb73d2/32.png) [@dacorb](https://forum.dynare.org/u/dacorb)\ **Post date:** [5 February 2021 09:24 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/13 "2021-02-05T09:24:07Z")
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 ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [5 February 2021 09:25 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/14 "2021-02-05T09:25:47Z")
That sounds reasonable. ---
**Author:** ![dacorb](https://forum.dynare.org/letter_avatar_proxy/v4/letter/d/bb73d2/32.png) [@dacorb](https://forum.dynare.org/u/dacorb)\ **Post date:** [5 February 2021 09:27 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/15 "2021-02-05T09:27:38Z")
So now, how do I perform that ? Just by comparing the gain of relative consumption between two dates for my two agents ? @jpfeifer ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [5 February 2021 09:35 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/16 "2021-02-05T09:35:59Z")
It’s more complicated as we are talking about welfare, so the path of utility matters. Usually, you do something like > [@Consumption Equivalence\_Welfare analysis](https://forum.dynare.org/t/consumption-equivalence-welfare-analysis/14268): > > Hi, I am trying to proceed with a welfare analysis. I have estimated the values of consumption equivalence for the 2 regimes as well as the values from the welfare equations, however i am not sure whether i need to compare the values of consumption equivalent or welfare values and determine the optimal policy. I read in previous posts that the change of sign matters, but for example in my case both regimes have negative sign for consumption equivalent. Which is the best policy, the one with… ---
**Author:** ![dacorb](https://forum.dynare.org/letter_avatar_proxy/v4/letter/d/bb73d2/32.png) [@dacorb](https://forum.dynare.org/u/dacorb)\ **Post date:** [5 February 2021 10:50 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/17 "2021-02-05T10:50:35Z")
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. ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [5 February 2021 13:27 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/18 "2021-02-05T13:27:01Z")
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. ---
**Author:** ![dacorb](https://forum.dynare.org/letter_avatar_proxy/v4/letter/d/bb73d2/32.png) [@dacorb](https://forum.dynare.org/u/dacorb)\ **Post date:** [5 February 2021 14:52 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/19 "2021-02-05T14:52:55Z")
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 ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [6 February 2021 10:10 UTC](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425/20 "2021-02-06T10:10:16Z")
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. [Next page](https://forum.dynare.org/t/measures-of-welfare-gains-losses/17425.md?page=2)