IV Regression with Possibly Uncorrelated Instruments

This paper proposes a closed-form linear IV estimator which allows endogenous covariates to be weakly correlated or un-correlated but mean-dependent on instruments. Identification rests on (1) a weak uncorrelatedness exclusion restriction and (2) a weak relevance condition where covariates are mean-dependent on instruments. The significant weakening of the relevance condition does not come at the cost of a stronger exclusion restriction. The estimator is root-n-consistent and asymptotically normal. Monte Carlo simulations show the estimator exploits unknown forms of both monotone and non-monotone identifying variation equally well, and it incurs less bias and size distortion relative to conventional IV methods when instruments are weak. An empirical example illustrates the practical usefulness of the estimator

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 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 in favour of the natural one that the parameter support be compact. 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.Comment: Third draft. Second draft: February 21, 2023. First draft: June 2019. More simulation results adde