Jacobian-free Efficient Pseudo-Likelihood (EPL) Algorithm

TL;DR

This paper introduces a Jacobian-free approach to efficiently compute the EPL estimator for dynamic discrete games, significantly reducing coding complexity while maintaining accuracy and speed.

Contribution

It develops a novel Jacobian-free algorithm combining numerical derivatives and Krylov methods, simplifying implementation for complex models.

Findings

The proposed method is computationally efficient.

Numerical experiments demonstrate good performance.

The approach reduces coding errors and complexity.

Abstract

This study proposes a simple procedure to compute Efficient Pseudo Likelihood (EPL) estimator proposed by Dearing and Blevins (2024) for estimating dynamic discrete games, without computing Jacobians of equilibrium constraints. EPL estimator is efficient, convergent, and computationally fast. However, the original algorithm requires deriving and coding the Jacobians, which are cumbersome and prone to coding mistakes especially when considering complicated models. The current study proposes to avoid the computation of Jacobians by combining the ideas of numerical derivatives (for computing Jacobian-vector products) and the Krylov method (for solving linear equations). It shows good computational performance of the proposed method by numerical experiments.