A Smoothed GMM for Dynamic Quantile Preferences Estimation

TL;DR

This paper introduces a smoothed GMM approach for estimating dynamic quantile preferences, enabling robust inference in models with non-linearities and dependent data, demonstrated through simulations and an empirical consumption model.

Contribution

It develops a novel smoothed GMM method for dynamic quantile estimation, establishing consistency and asymptotic normality under weak conditions.

Findings

Method performs well in finite samples

Successfully estimates risk attitude and substitution elasticity

Applicable to complex economic models

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.