Clustered Covariate Regression

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.