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When can regression be interpreted casually?
Must be all of the following; No reverse causality, all relevant confounders controlled (problem: some are unobservable), correct functional form (model correctly estimates conditional means)
Types of Observational Data
Cross-sectional: many units, one time period.
Time series: one unit, many time periods.
Panel (TSCS): many units over many time periods, allows between-unit and within-unit comparisons
Unit Fixed Effects Model
Focuses on within-unit over time variation, controls for all stable unit characteristics, observed or unobserved, coefficient of X = how Y changes within units as X changes, net of all fixed traits
Why Multiple Regression is essential
Allows control for many confounders simultaneously, allows Z to take many possible values, produces unbiased estimates if all relevant confounders included
Still limited by unobservable confounding and model assumptions