Fixed Effects Model
Fixed Effects Regression Model · Also known as: FE model, within estimator, least squares dummy variable, LSDV regression
The fixed effects (FE) model is the workhorse estimator for panel data when unobserved unit-specific characteristics are suspected to correlate with the regressors. By absorbing each entity's time-invariant heterogeneity into a separate intercept, FE isolates the causal effect of within-unit variation and eliminates omitted-variable bias from time-constant confounders.
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When to use it
Use fixed effects when your panel contains entity-specific unobserved heterogeneity that may correlate with the regressors (e.g., country culture, firm management quality, individual ability). FE is the preferred default in observational panel studies where omitted-variable bias from stable confounders is a concern. The Hausman test provides a formal guide: if it rejects the null, use FE over random effects. Do not use FE when the key regressor is time-invariant (e.g., gender, country of birth), because such variables are collinear with the fixed effects and their coefficients cannot be identified. FE is also less efficient than random effects when the strict exogeneity assumption holds, and it cannot be applied sensibly to cross-sectional data.
Strengths & limitations
- Eliminates bias from any time-constant unobserved confounders without requiring them to be measured or specified.
- Consistent estimation of beta even when fixed effects are correlated with the regressors — a key advantage over pooled OLS and random effects.
- Straightforward to implement as demeaned OLS or LSDV; results are easy to report and interpret.
- Naturally controls for all stable characteristics of the unit, making within-unit causal claims more credible than cross-sectional comparisons.
- Robust to a broad class of specification errors involving time-constant omitted variables.
- Time-invariant regressors (gender, country, legal origin) are perfectly collinear with entity dummies and drop from the model — their effects cannot be estimated.
- Efficiency loss relative to random effects when the exogeneity assumption truly holds, because between-unit variation is discarded.
- Requires a sufficient number of time periods per entity; with very short panels the within variation may be small and estimates imprecise.
- Does not address endogeneity from time-varying omitted variables or reverse causality — instrumental variables or dynamic panel methods are then needed.
- Incidental parameters problem in non-linear FE models (e.g., fixed-effects logit) can bias coefficients when T is small.
Frequently asked
What is the difference between fixed effects and random effects?
Fixed effects treats each entity's intercept as a free parameter to be estimated, making no assumption about its relationship to the regressors. Random effects treats entity intercepts as random draws from a distribution and assumes they are uncorrelated with the regressors — a stronger but more efficient assumption when valid. The Hausman test is the standard diagnostic to choose between them.
Can I estimate the effect of a time-invariant variable with a fixed effects model?
No. Time-invariant variables such as gender, country of origin, or legal system are perfectly collinear with the entity fixed effects and cannot be separately identified. If these variables are of interest, consider random effects, the Mundlak–Chamberlain correlated random effects approach, or a two-stage strategy.
Does fixed effects solve all endogeneity problems?
Only endogeneity arising from time-constant unobserved heterogeneity. Time-varying omitted variables, reverse causality, or measurement error in regressors are not addressed by FE. Instrumental variables or dynamic panel GMM estimators (Arellano-Bond) are needed in those situations.
Should I always cluster standard errors in a fixed effects model?
In most panel data applications, yes. Clustering by entity accounts for serial correlation within units over time, which is the dominant source of non-spherical errors in panels. Failing to cluster typically understates standard errors and produces misleadingly small p-values.
What is two-way fixed effects?
Two-way fixed effects includes both entity fixed effects (controlling for time-constant unit characteristics) and time fixed effects (controlling for period-specific shocks common to all units, such as a global financial crisis). It is appropriate when both sources of heterogeneity are plausible confounders.
Sources
- Baltagi, B. H. (2021). Econometric Analysis of Panel Data (6th ed.). Springer. ISBN: 978-3030538002
- Mundlak, Y. (1978). On the pooling of time series and cross section data. Econometrica, 46(1), 69–85. DOI: 10.2307/1913646 ↗
How to cite this page
ScholarGate. (2026, June 3). Fixed Effects Regression Model. ScholarGate. https://scholargate.app/en/econometrics/fixed-effects-model
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Arellano-Bond GMM estimatorEconometrics↔ compare
- Dynamic Panel Data ModelEconometrics↔ compare
- OLS RegressionEconometrics↔ compare
- Panel Data AnalysisEconometrics↔ compare
- Panel Hausman TestEconometrics↔ compare