Estimation with Errors in Variables via the Characteristic Function

55 Pages Posted: 11 Jun 2020

See all articles by Hamish Malloch

Hamish Malloch

The University of Sydney; Financial Research Network (FIRN)

Richard Philip

University of Sydney Business School

Stephen E. Satchell

University of Cambridge - Faculty of Economics and Politics

Date Written: May 18, 2020

Abstract

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.

Keywords: Error in Variables, Characteristic Function, CAPM, Beta

JEL Classification: C13, C22, C58, G12

Suggested Citation

Malloch, Hamish and Philip, Richard and Satchell, Stephen E., Estimation with Errors in Variables via the Characteristic Function (May 18, 2020). Available at SSRN: https://ssrn.com/abstract=3603907 or http://dx.doi.org/10.2139/ssrn.3603907

Hamish Malloch

The University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Richard Philip (Contact Author)

University of Sydney Business School ( email )

Cnr. of Codrington and Rose Streets
Sydney, NSW 2006
Australia

Stephen E. Satchell

University of Cambridge - Faculty of Economics and Politics ( email )

Austin Robinson Building
Sidgwick Avenue
Cambridge, CB3 9DD
United Kingdom
44 (0)1223 335213 (Phone)
44 (0)1223 335475 (Fax)

HOME PAGE: http://www.econ.cam.ac.uk/faculty/satchell/index.h

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