Adaptive Grids for the Estimation of Dynamic Models

Lanz, Andreas, Gregor Reich, and Ole Wilms (2022), “Adaptive Grids for the Estimation of Dynamic Models,” Quantitative Marketing and Economics, forthcoming.

62 Pages Posted: 18 Sep 2020 Last revised: 6 Jan 2022

See all articles by Andreas Lanz

Andreas Lanz

HEC Paris - Marketing

Gregor Reich

Tsumcor Research AG

Ole Wilms

University of Hamburg; Tilburg University - Tilburg University School of Economics and Management

Date Written: August 17, 2021

Abstract

This paper develops a method to flexibly adapt interpolation grids of value function approximations in the estimation of dynamic models using either NFXP (Rust, 1987) or MPEC (Su and Judd, 2012). Since MPEC requires the grid structure for the value function approximation to be hard-coded into the constraints, one cannot apply iterative node insertion for grid refinement; for NFXP, grid adaption by (iteratively) inserting new grid nodes will generally lead to discontinuous likelihood functions. Therefore, we show how to continuously adapt the grid by moving the nodes, a technique referred to as r-adaption. We demonstrate how to obtain optimal grids based on the balanced error principle, and implement this approach by including additional constraints to the likelihood maximization problem. The method is applied to two models: (i) the bus engine replacement model (Rust, 1987), modified to feature a continuous mileage state, and (ii) to a dynamic model of content consumption using original data from one of the world’s leading user-generated content networks in the domain of music.

Keywords: Numerical dynamic programming, mathematical programming with equilibrium constraints, r-adaptive grid refinement, equi-oscillation

JEL Classification: C25, C63

Suggested Citation

Lanz, Andreas and Reich, Gregor and Wilms, Ole, Adaptive Grids for the Estimation of Dynamic Models (August 17, 2021). Lanz, Andreas, Gregor Reich, and Ole Wilms (2022), “Adaptive Grids for the Estimation of Dynamic Models,” Quantitative Marketing and Economics, forthcoming., Available at SSRN: https://ssrn.com/abstract=2650994 or http://dx.doi.org/10.2139/ssrn.2650994

Andreas Lanz

HEC Paris - Marketing ( email )

Paris
France

Gregor Reich

Tsumcor Research AG ( email )

Switzerland

Ole Wilms (Contact Author)

University of Hamburg ( email )

Allende-Platz 1
Hamburg, 20146
Germany

HOME PAGE: http://www.olewilms.com

Tilburg University - Tilburg University School of Economics and Management ( email )

PO Box 90153
Tilburg, 5000 LE Ti
Netherlands

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