Parameterized expectations algorithm: how to solve for labor easily

Euler-equation methods for solving nonlinear dynamic models involve parameterizing some policy functions. We argue that in the typical macroeconomic model with valuable leisure, labor function is particularly convenient for parameterizing. This is because under the labor-function parameterization, the intratemporal first-order condition admits a closed-form solution, while under other parameterizations, there should be a numerical solution. In the context of a simulation-based parameterized expectations algorithm, we find that using the labor-function parameterization instead of the standard consumption-function parameterization reduces computational time by more than a factor of ten