Adaptive grids for the estimation of dynamic models

Andreas Lanz (), Gregor Reich () and Ole Wilms ()
Additional contact information
Andreas Lanz: HEC Paris
Gregor Reich: Tsumcor Research AG
Ole Wilms: University of Hamburg

Quantitative Marketing and Economics (QME), 2022, vol. 20, issue 2, No 3, 179-238

Abstract: 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, Econometrica: Journal of the Econometric Society, 55, 999–1033, 1987) or MPEC (Su & Judd, Econometrica: Journal of the Econometric Society, 80, 2213–2230, 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 (search for similar items in EconPapers)
JEL-codes: C25 C63 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s11129-022-09252-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:qmktec:v:20:y:2022:i:2:d:10.1007_s11129-022-09252-7

Ordering information: This journal article can be ordered from
http://www.springer. ... ng/journal/11129/PS2

DOI: 10.1007/s11129-022-09252-7

Access Statistics for this article

Quantitative Marketing and Economics (QME) is currently edited by Pradeep Chintagunta

More articles in Quantitative Marketing and Economics (QME) from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().