When should I use fixed effects in panel regression?

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AcadiFi · Accepted Answer

Fixed effects (FE) regression includes dummy variables for each entity (firm) or time period, controlling for time-invariant unobserved heterogeneity. The model: y_{i,t} = alpha_i + beta*x_{i,t} + e_{i,t}, where alpha_i is a firm-specific intercept absorbing all time-invariant firm characteristics (industry, headquarters location, founding era, management culture).

Mathematically, FE is equivalent to the 'within transformation': demean each variable by the firm's mean over time, then run OLS on deviations from means: (y_{i,t} - y_bar_i) = beta*(x_{i,t} - x_bar_i) + (e_{i,t} - e_bar_i). This eliminates any variable that doesn't vary within firms.

Use FE when: (1) you suspect unobserved time-invariant confounders correlated with X (omitted variable bias), (2) you have panel data with repeated observations per entity, (3) you care about within-entity variation (how does firm i's leverage change when its profitability changes).

For Zenith's panel of 500 firms over 20 years studying leverage, with pooled OLS, the coefficient on profitability might be -0.3 (more profitable firms are less levered). With firm FE, the coefficient becomes -0.05, much smaller—showing that cross-firm correlation was contaminating the pooled estimate. The within-firm relationship is weaker.

Drawbacks: FE can't identify effects of time-invariant variables (industry dummies drop out). Also, if your variable of interest has limited within-firm variation, FE estimates are imprecise. Hausman test compares FE vs RE: if Hausman rejects RE, use FE. In corporate finance research, firm+year FE is the default specification.

When should I use fixed effects in panel regression?

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