OLIVE: A simple method for estimating betas when factors are measured with error

We propose a simple and intuitive method for estimating betas when factors are measured with error: ordinary least squares instrumental variable estimator (OLIVE). OLIVE performs well when the number of instruments becomes large, whereas the performance of conventional instrumental variable methods becomes poor or even infeasible. In an empirical application, OLIVE beta estimates improve R² significantly. More important, our results help resolve two puzzling findings in the prior literature: first, the sign of average risk premium on the beta for market return changes from negative to positive; second, the estimated value of average zero‐beta rate is no longer too high.