Speedup algorithm: Modified policy iterations

We consider following random model without labor:

for

and

where and are error terms with mean zero.

We also consider the following random model with labor:

We approximate the following random model with labor:

for the same random processes of Q and A. L is replaced by Lstar that is constant and

is computed from FOC with respect to labor.

We implement both error bounds and modified policy iterations in the same way as

before when we compute each policy function.

Technically, we attach option 4 by modifying option 3 and add option 5 to option 1.