Model-Adaptive Approach to Dynamic Discrete Choice Models with Large State Spaces

Abstract

Estimation and counterfactual experiments in dynamic discrete choice models with large state spaces pose computational difficulties. This paper proposes a model-adaptive approach, based on the conjugate gradient (CG) method, to solve the linear system of fixed point equations of the policy valuation operator. We propose a model-adaptive sieve space, constructed by iteratively augmenting the space with the residual from the previous iteration. We show both theoretically and numerically that model-adaptive sieves dramatically improve performance. In particular, the approximation error decays at a superlinear rate in the sieve dimension, unlike a linear rate achieved using successive approximation. Our method works for both conditional choice probability estimators and full-solution estimators with policy iteration or Newton-Kantorovich iterations. We apply the method to analyze consumer demand for laundry detergent using Kantar's Worldpanel Take Home data. On average, our method is 80% faster than successive approximation and the exact equation solver in solving the dynamic programming problem, substantially reducing the computational cost of the Bayesian MCMC estimator.

Figures (9)

• Figure 1: Convergence Behavior of Model-Adaptive Approach
• Figure 2: Norms of residuals and approximation error for Bus Engine Replacement
• Figure 3: Sup-norm of Residuals
• Figure 4: $L_{2}$-Norm of Residuals
• Figure 5: Sup-norm of Approx. Error

Theorems & Definitions (65)

• Definition 1
• Remark 1
• Theorem 1
• Theorem 2
• Definition 2: $R$-Convergence ortega2000iterative
• Theorem 3: Superlinear Convergence
• Remark 2: Implications for Statistical Inference
• Theorem 4
• Theorem 5
• proof : Proof of \ref{['theorem: unique solution on nu']}