### (Steady State) Welfare

Posted:

**Thu Jul 13, 2017 8:18 pm**Dear all,

I want to calculate the welfare differences between two versions of my model ( in one model foreign aid is used for public investment, in the other it goes to households as a lump sum transfer).

In an ideal world I would use a consumption equivalent measure but as I do not know how to do this, and am short in time, I am trying to look at suboptimal ways to calculate welfare. I have never done this before and seem to be unable to find a paper/ lecture sheets/ information on how to set up such an analysis from scratch.

So I wanted to start as easy as possible and calculate the welfare differences of the steady states of the two models. I have the following utility function

U = E_0 \sum_{t=0}^{\infty} beta^t * [C_t^(1-sigma)/(1-sigma) - theta* (L_t^(1+\chi)/(1+\chi))]

This however always returns negative utility as sigma >1. If I then use the value function W = U + bet*W(+1); this will be negative as well. I thought that I used a rather standard utility function. Does this mean that these functions always return negative welfare or am I making a mistake somewhere?

For the next step I would want to start off with the steady state values of model (1) and then switch regimes and use model 2, simulate for more many periods, and "feed" the time series of the variables that come out of this simulation to the welfare function. I hope that this gives me transitional dynamics. As said, I am new to the welfare analysis thing. Is this a logically/ feasible way of looking at the transitional dynamics of switching regimes?

If anyone knows some material where this is done/ explained please let me know as well!

Thank you and all the best!

I want to calculate the welfare differences between two versions of my model ( in one model foreign aid is used for public investment, in the other it goes to households as a lump sum transfer).

In an ideal world I would use a consumption equivalent measure but as I do not know how to do this, and am short in time, I am trying to look at suboptimal ways to calculate welfare. I have never done this before and seem to be unable to find a paper/ lecture sheets/ information on how to set up such an analysis from scratch.

So I wanted to start as easy as possible and calculate the welfare differences of the steady states of the two models. I have the following utility function

U = E_0 \sum_{t=0}^{\infty} beta^t * [C_t^(1-sigma)/(1-sigma) - theta* (L_t^(1+\chi)/(1+\chi))]

This however always returns negative utility as sigma >1. If I then use the value function W = U + bet*W(+1); this will be negative as well. I thought that I used a rather standard utility function. Does this mean that these functions always return negative welfare or am I making a mistake somewhere?

For the next step I would want to start off with the steady state values of model (1) and then switch regimes and use model 2, simulate for more many periods, and "feed" the time series of the variables that come out of this simulation to the welfare function. I hope that this gives me transitional dynamics. As said, I am new to the welfare analysis thing. Is this a logically/ feasible way of looking at the transitional dynamics of switching regimes?

If anyone knows some material where this is done/ explained please let me know as well!

Thank you and all the best!