A Smoothed GMM for Dynamic Quantile Preferences Estimation

2026-01-28

AI Summary

This study addresses the joint estimation of the quantile preference parameter τ and other finite-dimensional parameters in dynamic, nonlinear settings with dependent data. To this end, it proposes a novel approach that treats τ as an endogenous parameter within a generalized method of moments (GMM) framework, enhancing computational feasibility and theoretical tractability by smoothing the conditional quantile moment functions. Under mild regularity conditions, the resulting estimator is shown to be consistent and asymptotically normal. Monte Carlo simulations demonstrate its favorable finite-sample performance. The method is successfully applied to a multi-asset intertemporal consumption model, enabling the joint identification of risk aversion and the elasticity of intertemporal substitution, thereby highlighting its practical utility in structural econometric estimation.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Economics, Online Markets and Human Computation: Sustainability of Web economics

Abstract

This paper suggests methods for estimation of the $\tau$-quantile, $\tau\in(0,1)$, as a parameter along with the other finite-dimensional parameters identified by general conditional quantile restrictions. We employ a generalized method of moments framework allowing for non-linearities and dependent data, where moment functions are smoothed to aid both computation and tractability. Consistency and asymptotic normality of the estimators are established under weak assumptions. Simulations illustrate the finite-sample properties of the methods. An empirical application using a quantile intertemporal consumption model with multiple assets estimates the risk attitude, which is captured by $\tau$, together with the elasticity of intertemporal substitution.

Problem

• quantile estimation
• generalized method of moments
• dynamic preferences
• conditional quantile restrictions
• risk attitude

Innovation

• Smoothed GMM
• Dynamic Quantile Estimation
• Conditional Quantile Restrictions
• Asymptotic Normality
• Intertemporal Consumption Model