TY  - RPRT
        AU  - Dong, Hao
AU  - Millimet, Daniel L.
        TI  - Embrace the Noise: It Is OK to Ignore Measurement Error in a Covariate, Sometimes
        PY  - 2023/Oct/
        PB  - Institute of Labor Economics (IZA)
        CY  - Bonn
        T2  - IZA Discussion Paper
        IS  - 16508
        UR  - https://www.iza.org/index.php/publications/dp16508
        AB  - 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.
        KW  - measurement error
KW  - errors-in-variables
KW  - asymptotics
        ER  -