Estimation with Errors in Variables via the Characteristic Function

Errors in variables in linear regression continue to be a major empirical issue in financial econometrics. We propose a method using the characteristic function (CF) to obtain estimates for linear models with errors in the variables. By assuming that the explanatory variable follows a flexible double-gamma distribution, we obtain closed-form expressions for the analytic CF of the data generating process. Through simulations, we show that our method performs well relative to existing techniques that address EIVs, including the most sophisticated CF-based techniques, the continuum generalized method of moments and nonparametric methods based on empirical cumulants. We further extend our CF technique to a multivariate setting where it continues to produce accurate estimates. We also provide guidance on implementing CF methods and apply the technique to estimating betas based on the capital asset pricing model.