ARBIMETRA LAB
Panel Random Effects
Estimates a panel model using Swamy-Arora variance components, with a Hausman comparison to fixed effects.
What it does
Estimates a panel model using Swamy-Arora variance components, with a Hausman comparison to fixed effects.
Use it when entity effects are plausibly unrelated to the regressors.
Data you need
- Dependent variable
- Independent variables
- Entity identifier
Supported data: Panel. Level: Advanced.
Formula and method
yᵢₜ − θᵢȳᵢ = (1−θᵢ)β₀ + (xᵢₜ − θᵢx̄ᵢ)′β + eᵢₜ
Variance components are estimated from a within and a between regression (Swamy-Arora). The data are then partly demeaned using θ, and OLS on that transformation gives the GLS estimates.
Assumptions
- Entity effects are uncorrelated with all regressors
Input checks
- More entities than coefficients
- One row per entity and period
How to read the result
θ near 1 behaves like fixed effects, and θ near 0 like pooled OLS.
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 0.1098, p = <0.0001. Entity variance share = 0.718.
- Hausman: H = 2.1314, p = 0.3445.
- The coefficient on value is statistically significant at the 5% level.
Limitations
- Biased if entity effects are correlated with regressors
Numerical validation
Validated 21 of 21 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 RE: value | 0.109781 | 0.10978115 | 1.5e-7 | 1e-5 | Published output of the R package plm (Grunfeld data) |
| Grunfeld RE: capital | 0.308113 | 0.30811298 | 1.7e-8 | 1e-5 | Published output of the R package plm (Grunfeld data) |
| Grunfeld RE: intercept | -57.834415 | -57.83441491 | 9.5e-8 | 1e-5 | Published output of the R package plm (Grunfeld data) |
| Equals explicit GLS | 0.10978115 | 0.10978115 | 2.6e-16 | 1e-9 | Independent NumPy calculation |
| Standard error equals explicit GLS covariance | 0.01048917 | 0.01048917 | 1.0e-17 | 1e-9 | Independent NumPy calculation |
| Convention check: plm's standard error is reproduced with its residual-variance scaling | 0.010493 | 0.01049266 | 3.4e-7 | 2e-4 | Published output of the R package plm (Grunfeld data); this tool scales by σ²(error) instead, a 0.04% difference |
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 does the Hausman test compare?
It checks whether fixed and random effects estimates differ systematically. A rejection suggests that random effects is inconsistent.
ARBIMETRA LAB is an educational and research tool. Results should be checked by the researcher and are not professional advice.