Panel Simple Linear Regression
Panel Data Simple Linear Regression · Also known as: panel SLR, longitudinal simple regression, two-way panel simple regression, fixed-effects simple linear regression
Panel simple linear regression models a continuous outcome as a linear function of a single predictor using data that track the same entities (individuals, firms, countries) across multiple time periods. It separates within-entity variation from between-entity variation, enabling control for unobserved time-invariant characteristics that would confound a plain cross-sectional regression.
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When to use it
Use panel simple linear regression when you have one continuous predictor, a continuous outcome, and repeated observations on the same entities over time. It is the right tool when you suspect unobserved entity heterogeneity that is correlated with the predictor (fixed effects) or when you want to improve efficiency by exploiting longitudinal structure (random effects). Do not use it when the panel is extremely short (T = 2 with small N makes coefficient estimation noisy), when the predictor has no within-entity variation (a time-invariant variable is wiped out by fixed effects), or when the true relationship requires more than one predictor — in that case use panel multiple linear regression.
Strengths & limitations
- Controls for all time-invariant unobserved confounders without measuring them explicitly.
- Exploits both cross-sectional and longitudinal variation, yielding more precise estimates than pure cross-sections.
- Fixed-effects estimator is consistent even when entity effects are correlated with the predictor.
- Simple and transparent — one slope coefficient captures the within-entity effect of the predictor.
- Compatible with unbalanced panels where entities have different numbers of time observations.
- Fixed effects absorb time-invariant predictors, so their individual effects cannot be estimated.
- Requires sufficient within-entity variation in the predictor; if x barely changes over time for most entities, the estimator becomes imprecise.
- Does not address time-varying confounders — only unobserved time-invariant heterogeneity is controlled.
- Short panels (small T) combined with a lagged dependent variable produce Nickell bias in fixed-effects estimation.
Frequently asked
Should I use fixed effects or random effects?
Run the Hausman test. If the test is significant (p < 0.05), the entity effects are correlated with the predictor and fixed effects is the consistent choice. Random effects is more efficient when that correlation is absent but gives biased estimates when it is present.
Why must I cluster standard errors?
Observations from the same entity are correlated over time. Ordinary (non-clustered) standard errors treat them as independent, which dramatically overstates precision. Clustering at the entity level corrects for this within-entity dependence.
What if my single predictor barely varies within entities?
Fixed effects identify the slope only from within-entity changes. If the predictor is nearly time-invariant for most entities, the within variation is small and the fixed-effects estimator will have very large standard errors — effectively uninformative. Consider random effects if entity effects and the predictor are plausibly uncorrelated, or acknowledge the identification limitation.
Can I use this with only two time periods per entity?
Yes, T = 2 is the minimum for fixed effects. With exactly two periods, the within estimator is equivalent to a first-difference estimator. Estimates are valid but may be imprecise if N (the number of entities) is also small.
When should I add more predictors?
If other observed variables confound the relationship between your predictor and outcome, include them — that is panel multiple linear regression. Omitting relevant confounders biases the slope even with fixed effects controlling for unobserved time-invariant heterogeneity.
Sources
- Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data (2nd ed.). MIT Press. ISBN: 978-0262232586
- Baltagi, B. H. (2021). Econometric Analysis of Panel Data (6th ed.). Springer. ISBN: 978-3030534875
How to cite this page
ScholarGate. (2026, June 3). Panel Data Simple Linear Regression. ScholarGate. https://scholargate.app/en/statistics/panel-simple-linear-regression
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.
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