First order approximation


I am aware that doing a first order approximation of the value function can give you incorrect results when performing welfare comparisons and that higher order approximations are needed. However, what if I do the following:

  1. Take a linear approximation of the model that doesn’t include the value function
  2. Using the approximated model, simulate a panel of data (say N=10,000 T=1,000).
  3. Calculate within period utility substituting the simulated data into the non-approximated utility function.
  4. For each N, calculate lifetime welfare by adding up the within utilities and successively discounting.
  5. Repeat 1-4 N-1 more times and average over the N’s.

Would this be appropriate? Thanks.