Clustered Covariate Regression

TL;DR

This paper introduces a clustering-based estimator for covariate regression that relaxes traditional sparsity and heterogeneity assumptions, providing robust estimation in complex economic models.

Contribution

The paper presents the GPE method, which drops sparsity and heterogeneity restrictions, and demonstrates its theoretical robustness and practical effectiveness through simulations and an empirical application.

Findings

GPE reduces bias effectively compared to existing estimators.

GPE maintains size control in simulations.

GPE performs well in empirical demand elasticity estimation.

Abstract

High covariate dimensionality is increasingly occurrent in model estimation, and existing techniques to address this issue typically require sparsity or discrete heterogeneity of the \emph{unobservable} parameter vector. However, neither restriction may be supported by economic theory in some empirical contexts, leading to severe bias and misleading inference. The clustering-based grouped parameter estimator (GPE) introduced in this paper drops both restrictions and maintains the natural one that the parameter support be bounded. GPE exhibits robust large sample properties under standard conditions and accommodates both sparse and non-sparse parameters whose support can be bounded away from zero. Extensive Monte Carlo simulations demonstrate the excellent performance of GPE in terms of bias reduction and size control compared to competing estimators. An empirical application of GPE to estimating price and income elasticities of demand for gasoline highlights its practical utility.