Computational Tricks for Solving a Stochastic RBC Model

1
Computational Tricks for Solving a Stochastic
RBC Model

• Michael Michaux
• (representing Wharton)

2
Outline

• Objective
• Model
• Computational tricks
• Using concavity of V
• Using continuous labor choice n
• Results
• Questions

3
Objective

• Speed-up computations in a Value Function
  Iteration Program
• Use 2 tricks
• Use concavity of the value function,
• Use FOC to make labor a continuous function of
  the state space variables.

4
RBC Formulation

• The stochastic RBC model can be written as

5
Recursive Formulation

• The Bellman Equation (BE) is

6
Using Concavity of V

• Trick 1 Reduce the search domain of
  according to whether the slope is
  positive/negative.
• Algorithm
• Evaluate the end points of the domain,
• Evaluate 2 consecutive points in the middle,
• Update the search domain according to the middle
  points.
• Note This method is of order log(n)

7
Using Concavity of V
8
Continuous Labor

• Trick 2 Solve analytically for the optimal
  labor choice for each possible combination of
  the state space, i.e. get

• Use the FOC for n

9
Continuous Labor

• Therefore solves the following nonlinear
  equation
• Note that for some combination of the solution
  space, there is no feasible solution, e.g. case
  of too high investment.

10
Continuous Labor
n increasing in Ai ? Income effect
11
Continuous Labor

• The BE with continuous labor is

12
Performance Results for Trick 1

• Using concavity and monotonicity yields the best
  results.

13
Performance Results for Trick 2

• Using the FOCs (when possible) improves
  performance.

14
Questions