Identifying Demand Elasticity Via Heteroscedasticity: A Panel GMM Approach to Estimation and Inference

Abstract

This paper introduces a panel GMM framework for identifying and estimating demand elasticities via heteroscedasticity. While existing panel estimators address the simultaneity problem, the state-of-the-art Feenstra/Soderbery (F/S) estimator suffers from inconsistency, inefficiency, and lacks a valid framework for inference. We develop a constrained GMM (C-GMM) estimator that is consistent and derive a uniform formula of its asymptotic standard error that is valid even at the boundary of the parameter space. A Monte Carlo study demonstrates the consistency of the C-GMM estimator and shows that it substantially reduces bias and root mean squared error compared to the F/S estimator. Unlike the F/S estimator, the C-GMM estimator maintains high coverage of confidence intervals across a wide range of sample sizes and parameter values, enabling more reliable inference.

Keywords: Demand Elasticity, Panel Data, Heteroscedasticity, GMM, Constrained Estimation