Why Fixed-Effects Models Can Make Estimates More Biased Than OLS

🔍 Main Claim:

The fixed-effects estimator is not benign. It is biased when the model's dynamics are misspecified and when omitted within-unit variation is correlated with a regressor. Moreover, fixed effects can amplify bias from dynamic misspecification and—when omitted time-invariant variables coexist with dynamic misspecification—can be more biased than a naive OLS model.

🧭 How the argument is demonstrated:

Formal argumentation and demonstrations show how different forms of misspecification interact to produce bias. The analysis focuses on two common problems:

• dynamic misspecification (incorrect treatment of time dependence), and
• omitted variables that are either time-invariant or vary over time and correlate with regressors.

📌 Key findings:

• The fixed-effects estimator is biased in the presence of dynamic misspecification and omitted within-unit variation correlated with a regressor.
• Fixed effects can amplify the bias introduced by dynamic misspecification.
• When omitted time-invariant variables and dynamic misspecifications are both present, fixed effects can be more biased than naive OLS.
• The Hausman test does not reliably identify the least-biased estimator when time-invariant and time-varying omitted variables or dynamic misspecifications exist.

🔎 Implications for applied researchers:

• Do not treat the fixed-effects estimator as a default remedy for omitted variables without a convincing case that dynamics are correctly specified.
• Avoid relying on the Hausman test alone for model selection under these types of misspecification.
• Greater attention should be paid to modeling dynamics appropriately before adopting fixed effects to absorb potentially omitted constant effects.

📣 Call to methodologists:

These results caution against simplistic defaults and invite further study of estimator properties under multiple simultaneous misspecifications. More methodological work is needed on how estimators behave when dynamics and omitted-variable structures are both uncertain.