Instrumental variable estimation via a continuum of instruments with an application to estimating the elasticity of intertemporal substitution in consumption

This study proposes new instrumental variable (IV) estimators for linear models by exploiting a continuum of instruments effectively. The effectiveness is attributed to the unique weighting function employed in the minimum distance objective functions, which enjoys attractive properties in relation to estimation efficiency. The proposed estimators enjoy analytical formulas, which are easily computable. The inferences drawn for these estimators are also straightforward, since their variance estimators for parameter inferences are of analytical forms. The proposed estimators are robust to weak instruments and heteroskedasticity of unknown form. Further, they are robust to high dimensionality of included and excluded exogenous variables. This approach conveniently overcomes the deficiency of conventional IV estimators in the literature on many weak instruments, where the theoretical properties of these estimators depend crucially on the interplay among an increasing number of instruments, unknown degrees of weak identification, and unknown reduced forms. Comprehensive Monte Carlo simulations reveal that the proposed estimators have excellent finite sample properties, outperforming the alternative estimators in a wide range of cases. The new estimation procedure is applied to estimate the elasticity of intertemporal substitution (EIS) in consumption, which is of central importance in macroeconomics and finance. Using the US quarterly data from the fourth quarter of 1955 to the first quarter of 2018, the estimates of EIS of our approach well exceed one and are statistically different from zero. These estimates are robust to model transformation, different sets of IVs, different data structures and data ranges.