2024/08/05 by Hao Dong, Daniel L. Millimet · 1 voice
Economics, Econometrics and Finance · Mathematics · Social Sciences · #Economics of Agriculture and Food Markets #Income, Poverty, and Inequality #Statistical Methods and Inference
paper · doi:10.1093/jrsssa/qnae069
openalex publication_date 2024/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27
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 ⌊Nδ⌋ of N observations with δ∈[0,1]. We show that OLS is consistent for δ<1 and is asymptotically normal and more efficient than IV for δ<0.5. Simulations and an application to the impact of body mass index on family income demonstrate the practical usefulness of this result.