TITLE:
On Approximating the Gradient of the Value Function
AUTHORS:
Alexandre Dmitriev
KEYWORDS:
Dynamic Participation Constrains, Numerical Algorithm, Recursive Contracts
JOURNAL NAME:
Theoretical Economics Letters,
Vol.9 No.1,
February
1,
2019
ABSTRACT: The optimality conditions for macroeconomic problems
with limited commitment often contain partial derivatives of the optimal value
function, corresponding to the outside option. This paper contributes to the
literature on recursive contracts by proposing an algorithm for approximating
the gradient of the value function using simulation-based methods. Our method
combines numerical solution and simulation of the model, Monte-Carlo
integration and numerical differentiation. It does not suffer from the curse of
dimensionality and is therefore convenient for models involving many state
variables. The algorithm inherits the speed and accuracy limitations of the
numerical solution method it relies on. Our accuracy analysis is limited to a
few classical examples from macroeconomic literature.