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

Thanks for the link!

I am using the occbin toolbox. From my understanding the linear piecewise solution method requires a first-order approximation around both regimes’ steady state.

What I am after is computing (assuming log utility)

g=\exp\left(\left(1-\beta\right)\left(E \left[V_{t}^{1}\right]-E\left[V_{t}^{0}\right]\right)\right)-1

Where I would take the unconditional expectation of the value functions under different policies, V_{t}^{1} and V_{t}^{0}, over the simulated moments. I have always computed consumption equivalent variation over simulated moments. Perhaps there is another way? This is also initial work and the consumption equivalent variation was the first welfare analysis that came to mind.

This is a tricky issue that I haven’t really thought about before. It’s not obvious that a linear quadratic approximation in this case is correct or sufficient due to the occasionally binding constraint.