Clustered Covariate Regression

High covariate dimensionality is an increasingly occurrent phenomenon in model estimation. A common approach to handling high-dimensionality is regularisation, which requires sparsity of model parameters. However, sparsity may not always be supported by economic theory or easily verified in some empirical contexts; severe bias and misleading inference can occur. This paper introduces a grouped parameter estimator (GPE) that circumvents this problem by using a parameter clustering technique. The large sample properties of the GPE hold under fairly standard conditions including a compact parameter support that can be bounded away from zero. Monte Carlo simulations demonstrate the excellent performance of the GPE relative to competing estimators in terms of bias and size control. Lastly, an empirical application of the GPE to the estimation of price and income elasticities of demand for gasoline illustrates the practical utility of the GPE.