Olive: A Simple Method for Estimating Betas When Factors Are Measured With Error

Abstract

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, while the performance of conventional instrumental variable methods becomes poor or even infeasible. In an empirical application, OLIVE beta estimates improve R-squared significantly. More importantly, 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.JEL Classifications: C30, G12.1

Optimally weighting higher-moment instruments to deal with measurement errors in financial return models

“…More precisely, we propose a new weighting of two well-known cumulant instruments originally designed to tackle errors-in-variables, which are the Durbin (1954) and Pal (1980) estimators, and use it as an input to the two-stage least squares (TSLS) and the generalized method of moments (GMM) estimations. Our new optimal instruments are in line with the works of Fuller (1987), Dagenais and Dagenais (1997), Cragg (1997), Lewbel (1997), Coën and Racicot (2007) and Meng et al (2011). It is well-known that the Durbin and Pal's instruments lack robustness (Cheng and Van Ness, 1999) and they thus tend to be neglected by the academics.…”

“…As indicated in (15), the vector of estimated coefficients of the explanatory variables is identical to the one resulting from a conventional TSLS procedure using the same set of instruments (Spencer and Berk, 1981). This result, overlooked by Dagenais and Dagenais (1997) and other more recent researchers on this topic (Meng et al, 2011), increases the usefulness of Equation (15) …”

“…In that respect, they resort to the residuals of the cointegrating vector pulling together consumption, asset wealth and labor income to solve the measurement error problem, these residuals being a strong predictor of market returns. Finally, Meng et al (2011) propose a simple method they call OLIVE for estimating market betas when factors are measured with errors in the setting of the C-CAPM.…”

Cumulant instrument estimators for hedge fund return models with errors in variables

“…As indicated in (22), the vector of estimated coefficients of the explanatory variables is identical to the one resulting from a conventional TSLS procedure using the same set of instruments (Spencer and Berk, 1981). This result, overlooked by Dagenais and Dagenais (1997) and other more recent researchers on this topic (Meng et al, 2011), increases the usefulness of Equation (22) …”

Econometric Analysis of Large Factor Models

“…Bai and Ng (2010) show that even if the true optimal weighting matrix is used, inconsistency is still obtained under large number of moments. In fact, with many moments, sparse weighting matrix such as an identity matrix will give consistent estimation, as is shown by Meng et al (2011).…”