@TechReport{iza:izadps:dp16508,
            	author={Dong, Hao and Millimet, Daniel L.},
            	title={Embrace the Noise: It Is OK to Ignore Measurement Error in a Covariate, Sometimes},
            	year={2023},
	month={Oct},
            	institution={Institute of Labor Economics (IZA)},
            	address={Bonn},
            	type={IZA Discussion Paper},
            	number={16508},
            	url={https://www.iza.org/publications/dp16508},
	abstract={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.},
	keywords={measurement error;errors-in-variables;asymptotics},
            }