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TL;DR: Not all measurement error is fatal in panel data. In a Two-Way Fixed Effects (TWFE) model:

• Constant and Time-Specific additive errors are harmless (absorbed by FEs).
• Unit-Specific additive errors create bias when interacting a continuous regressor with a post-treatment dummy (Continuous DiD).
• The Fix: You can eliminate this bias by including Unit × Post fixed effects or by using post-period centering (FWL residualization).

TL;DR: Not all measurement error is fatal in panel data. In a Two-Way Fixed Effects (TWFE) model:

• Constant and Time-Specific additive errors are harmless (absorbed by FEs).
• Unit-Specific additive errors create bias when interacting a continuous regressor with a post-treatment dummy (Continuous DiD).
• The Fix: You can eliminate this bias by including Unit × Post fixed effects or by using post-period centering (FWL residualization).

TL;DR: Not all measurement error is fatal in panel data. In a Two-Way Fixed Effects (TWFE) model:

• Constant and Time-Specific additive errors are harmless (absorbed by FEs).
• Unit-Specific additive errors create bias when interacting a continuous regressor with a post-treatment dummy (Continuous DiD).
• The Fix: You can eliminate this bias by including Unit × Post fixed effects or by using post-period centering (FWL residualization).