# Welfare Analysis -- First Order Approximation of Equilibrium Conditions and Second Order Approximation of Welfare

I have a pretty large model and I would like to compare different policy specifications. I want to compute the unconditional expectation of the value functions over a large simulation and then use that to compute the consumption equivalent variation. These value functions are defined recursively as

V_t = U( C_t, H_t ) + beta* E_t (V_t+1)

I am thinking that I can take a first order approximation of the equilibrium conditions and then take a second order approximation of the value function.

Questions:

1. This this something that I could do in Dynare? That is, linearize the equilibrium conditions and take a second order approximation of welfare in the same file?

2. Are there any other methods to conduct welfare analysis when the model is approximated to the first order?

Why do you want a first order approximation instead of a proper second order one? And why do you want to compute unconditional welfare and the consumption equivalent based on simulated moments?

You may want to look at https://github.com/JohannesPfeifer/DSGE_mod/tree/master/Born_Pfeifer_2018/Welfare