Which condition is part of the Gauss-Markov assumptions ensuring the least squares estimator is BLUE?

• A. Homoscedastic, uncorrelated errors with zero mean.
• B. Heteroscedastic, correlated errors.
• C. Nonlinear relationships between variables.
• D. Known variances for all errors.

Answer: (A)

For the least squares estimator to be BLUE, the disturbances in a linear model must be zero-mean, homoscedastic, and uncorrelated. The zero mean ensures the estimates are unbiased, so on average they hit the true coefficients. Homoscedasticity means the error variance is the same across all observations, which prevents some data points from being given disproportionate influence and keeps the estimator’s variance as small as possible among all linear unbiased estimators. Uncorrelated errors mean there’s no systematic relationship between the errors of different observations, so the information in one data point isn’t redundant with another, contributing to efficiency. If errors are heteroscedastic or correlated, the OLS variance can be larger than necessary, so it is no longer the best among linear unbiased estimators. Nonlinear relationships violate the linear-in-parameters requirement, which undermines the foundation that makes OLS BLUE. Knowing the exact error variances would point toward generalized least squares rather than the standard Gauss–Markov setup, where these variances are not assumed known.