A Simple Improvement of the IV‐estimator for the Classical Errors‐in‐Variables Problem
| Author | Jarle Møen,Jonas Andersson |
| Published date | 01 February 2016 |
| DOI | http://doi.org/10.1111/obes.12103 |
| Date | 01 February 2016 |
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©2015 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 78, 1 (2016) 0305–9049
doi: 10.1111/obes.12103
A Simple Improvement of the IV-estimator for the
Classical Errors-in-Variables Problem
Jonas Andersson† and Jarle Møen†
†Department of Business and Management Science, Norwegian School of Economics,
Hellevn. 30 N-5045, Bergen, Norway (e-mail: jonas.andersson@nhh.no, jarle.moen@nhh.no)
Abstract
Two measures of an error-ridden variable make it possible to solve the classical errors-in-
variable problem by using one measure as an instrument for the other. It is well known
that a second IV-estimate can be obtained by reversing the roles of the two measures. We
explore the optimal linear combination of these two estimates. In a Monte Carlo study, we
show that the gain in precision is significant. The proposed estimator also compares well
with full information maximum likelihood under normality. We illustrate the method by
estimating the capital elasticity in the Norwegian ICT-industry.
I. Introduction
It is well known that ordinary least squares1(OLS) is inconsistent and biased if one or
more explanatory variables are measured with error. It is also wellknown that instrumental
variables (IV) can be used to deal with the problem. Graduate text books in econometrics
typically present the classical errors-in-variables model where one explanatory variable
is measured with error and the measurement error is uncorrelated with all explanatory
variables in the model as well as with the unobserved disturbance.A second measurement
of the mismeasured variable is introduced, and it is assumed that the measurement error in
the second measure is uncorrelated with the measurement error in the first as well as with
all other variables including the disturbance.The second measure is then a valid instrument
for the first. Papers that have made important contributions using this technique include
Ashenfelter and Krueger (1994), Borjas (1995), Barron, Berger and Black (1997) and
Krueger and Lindahl (2001).
The favourite text book example of instrumental variables used to solve a measure-
ment error problem in economics is the analysis of returns to education by Ashenfelter
and Krueger (1994). Ashenfelter and Krueger simultaneously account for ability bias and
measurement errors by using a sample of twins. Identical twins are similar with respect
to family background and genetic endowment, but measurement errors in education are
JEL Classification numbers: C13, C30, C80
1Wehave received useful comments from Erik Biørn, Gernot Doppelhofer and Arngrim Hunnes. We are grateful
to Anne Liv Scrase for proofreading the manuscript.
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