Parsimonious Estimation with Many Instruments

We suggest a way to perform parsimonious instrumental variables estimation in the presence of many, and potentially weak, instruments. In contrast to standard methods, our approach yields consistent estimates when the set of instrumental variables complies with a factor structure. In this sense, our method is equivalent to instrumental variables estimation that is based on principal components. However, even if the factor structure is weak or nonexistent, our method, unlike the principal components approach, still yields consistent estimates. Indeed, simulations indicate that our approach always dominates standard instrumental variables estimation, regardless of whether the factor relationship underlying the set of instruments is strong, weak, or absent.