X. Liu and Z. Cui, 2011, Approximation Errors of Perturbation Methods in Solving a Class of DSGE Models, Computational Economics, 38(2), 107-128. [Link]
On the one hand
It has been shown that the standard numerical method generates quite accurate numerical solution in solving DSGE models with the conventional distributions when policy functions (solutions) do not have kinks.
Standard numerical method:
The perturbation methods using the 2nd-order approximation around the non-stochastic steady state [Schmitt-Grohé, and Uribe (2004)].
Conventional distribution:
On the other hand
The conventional distribution may generate spurious welfare implications. In realizing this, Lucas assumed that the logarithm of exogenous shocks follows a normal distribution with a negative mean:
In our paper,
We show that standard methods generate large approximation errors in solving DSGE models with Lucas distributions.
We follow Schmitt-Grohé and Uribe (2004) and derive the mathematical equations for DSGE models with Lucas distributions.
We show the modifications to the existing Matlab programs
We apply the modified code to a model with the closed form solution and show large approximation errors
Major reference
Schmitt-Grohé, S., and Uribe, M. (2004). Solving Dynamic General Equilibrium Models Using A Second-order Approximation to The Policy Function. Journal of Economic Dynamics and Control, 28, 755–775.