Optimal Linear Instrumental Variables Approximations

This paper studies the identification and estimation of optimal linear approximation a structural regression function. The parameter in is called Optimal Linear Instrumental Variables Approximation (OLIVA). shows that necessary condition for standard inference on OLIVA also sufficient existence an IV estimand model. instrument unknown may not be identified. A Two-Step (TSIV) estimator based Tikhonov regularization proposed, which can implemented by routines. We establish asymptotic normality TSIV assuming neither completeness nor instrument. As important application our analysis, we robustify classical Hausman test exogeneity against misspecification discuss extensions to weighted least squares criteria. Monte Carlo simulations suggest excellent finite sample performance proposed inferences. Finally, empirical estimating elasticity intertemporal substitution (EIS) with US data, obtain estimates are much larger than their counterparts, robust failing reject null hypothesis real interest rates.