Title: Estimation of the CAPM with measurement error
Authors: Anastasia Morozova - University of Konstanz (Germany) [presenting]
Winfried Pohlmeier - University of Konstanz (Germany)
Abstract: The aim is to analyze the impact of measurement errors in the market portfolio on the estimates of the CAPM. In our theoretical set-up, we consider different types of measurement error and derive the consequences for the estimation of the CAPM parameters. Unlike traditional errors-in variable models, the different types of measurement error we introduce are theory based by and result directly from misspecifications of the market supply. We show that besides the well-known attenuation bias for the CAPM betas the CAPM alphas are upward biased leading to spurious excess returns. By exploding cross-equation restriction, we can show that the parameters CAPM with measurement error are identifiable without further instruments. In our Monte Carlo study, we investigate the bias for the CAPM parameters depending on type and size of the measurement error. We derive the conditions under which the true model parameters are feasible. As one of the identification strategies, we consider Instrumental Variable regression in case of many and/or weak instruments constructed from past asset returns. Since the dimensionality of this instrument set may be comparable to the sample size, the regularization and shrinkage techniques are used to obtain and improve the estimates of the model.