In terms of the consequences for the validity of the estimated coefficients and the validity of the t-values and standard errors, which is the more problematic issue: endogeneity, or heteroskedasticity?

Question

BlackTom AI · Accepted Answer

When considering the consequences for the validity of estimated coefficients and the validity of t-values and standard errors, we must weigh how each issue affects both consistency and inference.
Option 1: Heteroskedasticity. In the presence of heteroskedasticity, the ordinary least squares (OLS) estimates of the coefficients remain unbiased and consistent (assuming exogeneity of regressors), and they are still efficient in the sense of being the best linear unbiased estimates only under homoskedasticity. However, the usual standard errors and t-values become unreliable because the classic OLS standard error formulas assume constant variance of the error term. Therefore, while the coefficient estimates themselves are not biased, inference based on t-tests and confidence intervals is distorted unless robust standard errors are used. In short, heteroskedasticity primarily undermines inference rather than the unbiasedness of the coefficient estimates itself.
Option 2: Endogeneity. Endogeneity occurs when an explanatory variable is correlated with the error term, perhaps due to omitted variables, measurement error, or simultaneity. This correlation causes the OLS estimator of the coefficients to be biased and inconsistent in large samples, meaning that both the coefficient estimates and any standard errors derived under the assumption of exogeneity are invalid. Consequently, t-values and p-values become unreliable, and even large-sample asymptotics do not guarantee correct inference. This represents a fundamental violation that contaminates both the estimates and the inference drawn from them.
Comparative takeaway. While heteroskedasticity corrupts the reliability of standard errors and test statistics, it does not necessarily bias the coefficient estimates themselves (under exogeneity). Endogeneity, on the other hand, corrupts the very aim of OLS by biasing the coefficient estimates and rendering standard inference invalid. In terms of overall impact on the core goals of estimation (unbiased/consistent coefficients and valid inference), endogeneity is the more problematic issue.

In terms of the consequences for the validity of the estimated coefficients and the validity of the t-values and standard errors, which is the more problematic issue: endogeneity, or heteroskedasticity?单项选择题

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