When A Factor Is Measured with Error: The Role of Conditional Heteroskedasticity in Identifying and Estimating Linear Factor Models

Abstract

A new method is proposed for estimating linear triangular models, where identification results from the structural errors following a bivariate and diagonal GARCH(1,1) process. The associated estimator is a GMM estimator shown to have the usual √T-asymptotics. A Monte Carlo study of the estimator is provided as is an empirical application of estimating market betas from the CAPM. These market beta estimates are found to be statistically distinct from their OLS counterparts and to display expanded cross-sectional variation, the latter feature offering promise for their ability to provide improved pricing of cross-sectional expected returns.Measurement error; triangular models; factor models; heteroskedasticity; identification; many moments; GMM