ARBIMETRA LAB
Panel Fixed Effects
Controls for stable differences between entities using the within transformation, with optional time effects.
What it does
Controls for stable differences between entities using the within transformation, with optional time effects.
Use it when unobserved entity traits may be related to the regressors.
Data you need
- Dependent variable
- Independent variables
- Entity identifier
Optional: Time identifier
Supported data: Panel. Level: Advanced.
Formula and method
yᵢₜ − ȳᵢ = (xᵢₜ − x̄ᵢ)′β + (εᵢₜ − ε̄ᵢ)
Each variable has its entity mean subtracted, which removes every stable difference between entities. OLS on the transformed data gives the same slopes as including a dummy for each entity, and degrees of freedom are adjusted to match.
Assumptions
- Regressors are strictly exogenous given the entity effect
Input checks
- At least two entities
- One row per entity and period
- Variables must change within entities
How to read the result
Coefficients describe changes within an entity over time.
Worked example
Illustrative run on Grunfeld investment panel. These figures are the actual output of this model on that example, and they say nothing about your own data.
- value: coefficient 0.1101, p = <0.0001. Within R² = 0.7668.
- The within-entity association for value is statistically significant at the 5% level.
Limitations
- Cannot estimate variables that never change within an entity
Numerical validation
Validated 19 of 19 automated checks passed, including numerical results, invalid input, missing values, small samples, constant variables, charts and the interpretation text.
| Check | Reference | Result | Abs. error | Tolerance | Source |
|---|---|---|---|---|---|
| Grunfeld within: value | 0.110124 | 0.1101238 | 2.0e-7 | 1e-5 | Published output of the R package plm (Grunfeld data) |
| Grunfeld within: capital | 0.310065 | 0.31006534 | 3.4e-7 | 1e-5 | Published output of the R package plm (Grunfeld data) |
| Grunfeld within s.e.: value | 0.011857 | 0.01185669 | 3.1e-7 | 1e-4 | Published output of the R package plm (Grunfeld data) |
| Equals least-squares dummy variables | 0.1101238 | 0.1101238 | 1.2e-14 | 1e-9 | Independent NumPy calculation |
| Two-way effects equal dummy variables | 0.11771586 | 0.11771586 | 7.9e-15 | 1e-8 | Independent NumPy calculation |
Computed with python 3.13.2, numpy 2.2.5, scipy 1.14.1, pandas 2.3.3, statsmodels 0.14.4, scikit-learn 1.7.0, in your browser. A passing check confirms the listed comparison only. It does not make any result suitable for your data, and it is not a claim of equivalence with other statistical software.
Questions
What do fixed effects remove?
All stable differences between entities, whether or not they are measured.
ARBIMETRA LAB is an educational and research tool. Results should be checked by the researcher and are not professional advice.