Concept Architecture
Concept
Theoretically, Fixed Effects is a statistical modelling approach that estimates the effects of observed explanatory variables while controlling for all unobserved characteristics that remain constant within each individual, group or observational unit over time. It is founded on panel data econometrics and exists to produce unbiased estimates when time-invariant unobserved heterogeneity is correlated with the explanatory variables. In health economics, fixed effects models are widely used for analysing longitudinal patient, provider and regional data.
Mathematically, the fixed effects model represents the outcome as a function of observed covariates, an individual-specific intercept and a random error term. Estimation is achieved by transforming the data to eliminate the individual-specific effect, most commonly through the within transformation or first-difference estimation. Regression coefficients are then estimated using ordinary least squares on the transformed data.
In practice, fixed effects models are implemented using repeated observations collected for the same individuals, healthcare providers or geographical areas over time. They are commonly applied in health economics to evaluate policy changes, estimate treatment effects from observational panel data and analyse longitudinal healthcare costs, utilisation and health outcomes.
Purpose
Used to estimate causal associations from longitudinal data while controlling for unobserved time-invariant confounding, improving the validity of policy evaluation and observational health economic analyses.
Mathematical Formulae
Primary Formula
y?? = �? + ?X?? + �??
where:
- y?? = outcome for individual i at time t
- �? = individual-specific fixed effect
- ? = vector of regression coefficients
- X?? = explanatory variables
- �?? = random error term
Supporting Formulae
Within transformation:
(y?? ? y??) = ?(X?? ? X??) + (�?? ? �??)
Least squares estimator:
?? = (X?X)??X?y
where the estimation is performed on the transformed data.
Related Mathematical Methods
- Panel Data Regression
- Within Estimator
- First-Difference Estimation
- Ordinary Least Squares
- Hausman Test
- Difference-in-Differences
- Generalised Least Squares
Example
A health economist analyses annual healthcare expenditure for 2,500 patients observed over six years to evaluate the impact of a new disease management programme. A fixed effects model controls for unobserved patient characteristics that remain constant over time, such as genetic predisposition and early-life health status. The estimated treatment coefficient represents the average within-patient change in expenditure attributable to the programme after accounting for these fixed characteristics.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| AVERAGEIFS | =AVERAGEIFS(C:C,A:A,A2) | Calculate individual-specific means for within transformation |
| SUMPRODUCT | =SUMPRODUCT(B2:B101,C2:C101) | Matrix calculations used in regression estimation |
| LINEST | =LINEST(E2:E101,F2:H101,TRUE,TRUE) | Estimate regression coefficients on transformed panel data |
| MMULT | =MMULT(A1:C3,D1:F3) | Matrix operations for coefficient estimation |
VBA (Optional)
Automate fixed effects panel regression by transforming longitudinal data, estimating within-effects models and generating regression summaries for health economic evaluations.
Sources
- Wooldridge JM. Econometric Analysis of Cross Section and Panel Data.
- Baltagi BH. Econometric Analysis of Panel Data.
- Greene WH. Econometric Analysis.
- Angrist JD, Pischke JS. Mostly Harmless Econometrics.
- Briggs AH, Claxton K, Sculpher MJ. Decision Modelling for Health Economic Evaluation.
Related Concepts (2)
Library
Publications
1
Statistical Analysis of Cost-Effectiveness Data — Willan & Briggs, 1st Edition ed., 2006 (John Wiley & Sons)
A synthesis of statistical methods for analysing cost-effectiveness data, including net-benefit regression, confidence intervals for the ICER, cost-effectiveness acceptability curves, and covariate adjustment. Part of the Wiley Statistics in Practice series.
BookView source →
Frequently Asked Questions (6)
What is a fixed effects model?
A panel data modelling approach estimating a separate intercept for each individual or group, controlling for all its time-invariant characteristics.
Source: Wooldridge 2010
How does a fixed effects model control for stable individual differences?
A fixed effects model, applied to data following the same individuals or groups over time, estimates a separate baseline for each one and so absorbs everything about them that does not change. By comparing each individual only with themselves across time, it controls for all their stable characteristics, measured or not, removing them as a source of confounding. This is powerful for isolating the effect of factors that do vary over time, at the cost of learning nothing about the stable traits it absorbs. Comparing individuals with their own past is its method. Kirkwood and Sterne (2003) describe this.
Source: Kirkwood & Sterne 2003
How does a fixed effects model work?
A fixed effects model works by including a separate intercept for each unit, or equivalently by analysing deviations from each unit's own mean over time, so that all time-invariant characteristics of the unit are held constant and the estimated effects rest on within-unit variation. This eliminates confounding by stable unit-level factors. So a fixed effects model works by absorbing each unit's fixed characteristics into its own intercept and using only the variation within units across time to estimate effects, which controls for unobserved time-constant differences between units, though it cannot estimate the effects of variables that do not change within units.
Source: Wooldridge 2010
What does a fixed effects model control for?
A fixed effects model controls for all time-invariant characteristics of each unit, whether observed or unobserved, because giving each unit its own intercept removes any stable differences between units from the comparison. It thus addresses confounding by factors that do not change over time within a unit. So a fixed effects model controls for unobserved, time-constant confounders, which is its key strength, since it removes their influence without needing to measure them, though it does not control for confounders that vary within units over time, which must be addressed separately.
Source: Wooldridge 2010
What are the limitations of a fixed effects model?
The limitations of a fixed effects model include that it cannot estimate the effects of variables that do not vary within units, since those are absorbed by the unit intercepts; that it relies only on within-unit variation, which can be limited, reducing precision; and that it does not control for time-varying confounders. So a fixed effects model is used with awareness that it addresses only time-constant confounding and cannot assess stable characteristics, and that its reliance on within-unit variation may reduce efficiency, which is why the choice between fixed and random effects depends on the questions of interest and on assumptions about the unit-level effects.
Source: Wooldridge 2010
How does a fixed effects model differ from a random effects model?
A fixed effects model estimates a separate intercept for each unit and uses only within-unit variation, controlling for all time-invariant unit characteristics but assuming nothing about their distribution, while a random effects model treats the unit-specific effects as drawn from a distribution, using both within- and between-unit variation and allowing estimation of time-invariant variables, but assuming the unit effects are uncorrelated with the predictors. So the two differ in how they treat unit-level effects, with fixed effects being more robust to unobserved time-constant confounding and random effects more efficient but reliant on a stronger assumption, and the choice depends on that assumption and the analytic goals.
Source: Wooldridge 2010
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 16 Dec 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/fixed-effects
- Term code
- HE-ES-SA-067
Stable URI · Machine-readable · Resolvable · CC BY 4.0