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 utilizing a continuum of instruments. The effectiveness of the new estimation method is attributed to the unique weighting function employed in the minimum distance objective functions. The proposed estimators enjoy analytical formulas and are nuisance-parameterfree, avoiding the choice of an arbitrary number of moments or bandwidth in previous literature. They are robust to weak instruments and heteroskedasticity of unknown form. Moreover, they are robust to the high dimensionality of included and excluded exogenous variables. Further, inference drawn from these estimators is also straightforward. Comprehensive Monte Carlo simulations confirm that the proposed estimators exhibit excellent finite-sample properties and outperform alternative estimators over a wide range of cases. The new estimation procedure is then applied to gauge the elasticity of intertemporal substitution (EIS) in consumption, a parameter of central importance in both macroeconomics and finance. For quarterly data of the U.S. from Q4 1955 to Q1 2018, the EIS estimates obtained through our approach exceed one and are statistically significant. These findings persist across model transformations, distinct sets of IVs, various data structures, and different data ranges.