%0 Report
        %A Dong, Hao
%A Millimet, Daniel L.
        %T Embrace the Noise: It Is OK to Ignore Measurement Error in a Covariate, Sometimes
        %D 2023
        %8 2023 Oct
        %I Institute of Labor Economics (IZA)
        %C Bonn
        %7 IZA Discussion Paper
        %N 16508
        %U https://www.iza.org/publications/dp16508
        %X In linear regression models, measurement error in a covariate causes Ordinary Least Squares (OLS) to be biased and inconsistent. Instrumental Variables (IV) is a common solution. While IV is also biased, it is consistent. Here, we undertake an asymptotic comparison of OLS and IV in the case where a covariate is mismeasured for [N&#948;] of N observations with &#948;&#8201;&#8714;&#8201;[0, 1]. We show that OLS is consistent for &#948; < 1 and is asymptotically normal and more efficient than IV for &#948; < 0.5. Simulations and an application to the impact of body mass index on family income demonstrate the practical usefulness of this result.
        %K measurement error
%K errors-in-variables
%K asymptotics