Fixed Effects Models

Causal Inference Design

Regression Discontinuity (RD) and Interrupted Time Series (ITS) are powerful, but they require specific triggers or cutoffs. Many public policy questions involve gradual changes that don’t map neatly onto a single moment.

The Fixed Effects Solution

FE doesn’t need a cutoff. Instead, it leverages panel data—multiple observations of units over time. By observing a unit repeatedly, we can compare it to itself, eliminating stable unit-based confounders like organizational culture or demographics.

Public Safety

Does changing officer headcount affect crime? FE compares each city to its own history, filtering out stable differences between high-crime and low-crime cities.

Education Funding

Does funding impact achievement? FE isolates within-district fluctuations, removing the bias of stable socio-economic differences between districts.

Model Specification

The standard Fixed Effects model estimates the effect of x on y by controlling for unit-specific intercepts:

                    # Example R Code for Fixed Effects
                    library(fixest)
                    model <- feols(outcome ~ treatment | unit_id + year, data = panel_df)
                    summary(model)
                

Note: Your independent variables must vary within units over time to be estimable in an FE framework.