OLIVE : A Simple Method for Estimating Betas When Factors Are Measured with Error

We propose a simple method for estimating betas (factor loadings) when factors are measured with error: Ordinary Least-squares Instrumental Variable Estimator (OLIVE). OLIVE is intuitive and easy to implement. OLIVE performs well when the number of instruments becomes large (can be larger than the sample size), while the performance of conventional instrumental variable methods and two-step GMM becomes poor or even infeasible. OLIVE is especially suitable for estimating asset return betas, since this is often a large N and small T setting. Intuitively, since all asset returns vary together with a common set of factors, one can use information contained in other asset returns to improve the beta estimate for a given asset. We apply OLIVE to modify the Fama-MacBeth method and reexamine the (C)CAPM. We find that in regressions where macroeconomic factors are included, using OLIVE instead of OLS beta estimates improves the R-squared significantly (e.g., from 31% to 80%). More importantly, our results based on OLIVE beta estimates help to resolve two puzzling findings in the prior literature: first, the sign of the average risk premium on the beta for the market return changes from negative to positive, consistent with the theory; second, the estimated value of average zero-beta rate is no longer too high (e.g., from 5.19% to 1.91% per quarter)