1. Adaptive Grids for the Estimation of Dynamic Models
- Author
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Ole Wilms, Gregor Reich, Ecole des Hautes Etudes Commerciales (HEC Paris), HEC Paris Research Paper Series, Research Group: Finance, and Department of Finance
- Subjects
History ,Mathematical optimization ,Polymers and Plastics ,Computer science ,Economics, Econometrics and Finance (miscellaneous) ,0211 other engineering and technologies ,Structure (category theory) ,mathematical programming with equilibrium constraints ,Equioscillation ,02 engineering and technology ,Industrial and Manufacturing Engineering ,JEL: C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C63 - Computational Techniques • Simulation Modeling ,Dynamic discrete choice models ,Bellman equation ,0502 economics and business ,050207 economics ,Business and International Management ,r-adaptive grid refinement ,Balanced Errors ,computer.programming_language ,Marketing ,021103 operations research ,equi-oscillation ,05 social sciences ,Grid ,Adaptive Grids ,Dynamic models ,numerical dynamic programming ,Feature (computer vision) ,[SHS.GESTION]Humanities and Social Sciences/Business administration ,Node (circuits) ,computer ,JEL: C - Mathematical and Quantitative Methods/C.C2 - Single Equation Models • Single Variables/C.C2.C25 - Discrete Regression and Qualitative Choice Models • Discrete Regressors • Proportions • Probabilities ,Interpolation ,Rust (programming language) - 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 Econom etric Society, 55, 999– 1 033, 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.
- Published
- 2020