Instruction: Provide a detailed explanation of the Fixed Effects model, including its assumptions, implementation, and when it is most appropriately used in causal inference.
Context: This question tests the candidate’s knowledge of handling panel data using Fixed Effects models to control for variables that are not observed but vary across entities and over time. The response should cover the mathematical foundation of the model, how it differs from Random Effects models, and its limitations in causal inference. Candidates should also discuss practical scenarios where this model would be preferable.