Lernportal

Fixed effects model

A fixed effects (FE) model is a statistical method that measures the impact of a policy by following the same farms over several years and comparing each farm to itself. By focusing only on changes over time within each farm, FE models isolate how variations in CAP support or other time‑varying factors are associated with changes in outcomes (such as income, productivity or environmental performance), while automatically controlling for all farm characteristics that remain constant over time.

Page contents

Male farmer using tablet in rapeseed field for digital tax record keeping

Basics

In a nutshell

A fixed effects (FE) model is a statistical method used to estimate the effect of a policy by following the same farms over several years. Instead of comparing different farms to each other, the model compares each farm to itself over time. This automatically factors out stable farm traits (such as soil quality or location) from the analysis, whether or not these characteristics are observed. FE models isolate the relationship between changes in a policy (e.g., CAP payments) and changes in outcomes (income, productivity, environmental indicators) within each farm. They rely entirely on within-farm variation.

A simple one way FE model looks like:

Y_it=α_i+βD_it+γX_it+ε_it

A two way FE model adds year effects:

Y_it=α_i+λ_t+βD_it+γX_it+ε_it

α_i: farm‑specific characteristics that do not change over time
λ_t: year‑specific shocks (e.g. weather, macro trends)
D_it and X_it: variables that change over time
Y_it: outcome for farm i in year t

FE models let us focus on ‘before-and-after’ changes within the same farm, instead of comparing different farms that might not be comparable. This makes the estimates more credible because long‑standing differences between farms cannot bias the results.

Key assumptions include:

All time‑invariant unobserved factors are absorbed by the farm fixed effects.
Time‑varying unobserved factors that affect both support and outcomes are either negligible or adequately controlled for by observed covariates and year effects.
The relationship between explanatory variables and the outcome is correctly specified (e.g. linear in parameters), and there is sufficient variation over time in the key variables (support levels, outcomes).

FE strengthens causal interpretation compared with simple cross-sectional OLS, but it does not fully guarantee causality when important time‑varying confounders are missing.

Pros and cons

Advantages	Disadvantages
FE models control for all stable farm differences: soil quality, altitude, long‑run management style, historical factors, etc., even if not observed.	Cannot control for unobserved factors that change over time and affect both support and outcomes (e.g. weather shocks interacting with policy, changes in management quality, new technologies adopted for reasons unrelated to CAP).
Useful for universal or widely applied measures (e.g. BISS, eco-schemes), where there is no obvious cross‑section control group, but there is variation over time in payment levels or rules.	Cannot estimate the impact of variables that do not change within a farm (e.g. constant soil type, permanent region code, fixed altitude), because these are absorbed by the farm FE.
Particularly suitable for panel data such as FADN/FSDN, where farms may be observed for several consecutive years, enabling within-farm comparisons over time.	Requires sufficiently long and good‑quality panels; with very short panels or many missing values, estimates become unstable.
	Still not a fully causal method: if time‑varying unobserved confounders are important, FE estimates may remain biased.

Evaluators should therefore view FE models as a powerful tool for identifying correlations while controlling for unobserved, time-invariant factors, but not as a replacement for well-designed causal strategies when high-stakes policy decisions are involved.

When to use?

Use FE models when you have panel data with the same units (farms) across three or more years and need to control for constant differences across farms. FE is especially appropriate for broadly applied policies (universal programmes) or when stable, unobserved factors are likely to bias simpler cross-sectional analyses.

Preconditions

To use FE models in a credible and meaningful way, national CAP evaluators need:

Panel data that track the same farms over multiple years.
Sufficient variation over time in both outcomes and key explanatory variables (e.g. changes in payment amounts, introduction of new measures, reforms of eligibility rules).
A large enough sample of farms observed consistently across the period to ensure reliable estimation.
Basic econometric competencies, including running panel‑data regressions, interpreting fixed‑effect coefficients and conducting standard diagnostic checks.
A solid understanding of the policy context, particularly the timing, design and implementation of CAP instruments, to correctly interpret which policy changes align with observed changes in outcomes.

When to use this technique in the context of the CAP Strategic Plan assessment

FE models are suited for assessing the effects of universal or widely applied measures (e.g. BISS, eco-schemes) when no clear cross‑sectional control group exists, provided there is meaningful variation over time in payment levels or rules.

FE models are particularly useful for:

Evaluating the effects of overlapping CAP interventions (e.g. BISS, CRISS, eco‑schemes).
Analysing regions where all farms receive support, making treatment-control comparisons difficult.
Examining long‑term impacts across successive policy changes.

Step-by-step

Step 1 – Assemble the panel dataset

Construct a panel in which the same farms (or territorial units) are observed across several consecutive years. Include:

i) outcome variables (e.g. farm income, productivity, emissions proxies)
ii) CAP support variables (by measure, payment type, intensity)
iii) time‑varying controls (e.g. input prices, weather indices where available, herd/flock size, crop mix)

Step 2 – Specify the regression model

Define a regression where:

i) the outcome is a farm‑level (or area‑level) indicator;
ii) key explanatory variables include CAP support and relevant controls; and
iii) farm fixed effects (αᵢ) and year fixed effects (λₜ) are included to absorb all time‑invariant farm characteristics and common year‑specific shocks.

Step 3 – Estimate the model

Use standard panel‑data estimation procedures (e.g. the ‘within’ estimator in Stata or R). The FEs themselves are not of substantive interest; the focus should be on the coefficients for CAP support and other time‑varying variables.

Step 4 – Check the specification and diagnostics

Verify that there is sufficient within‑farm variation in both support variables and outcomes. Inspect residuals (1) and test for heteroskedasticity (2) and serial correlation (3), adjusting standard errors (4) accordingly (e.g. clustering at the farm or regional level). Consider adding lagged outcomes (5) or interaction terms when policy effects are expected to materialise with a delay or to differ by farm type.

Residuals: The difference between the observed value of the outcome and the value predicted by the model.
Heteroskedasticity: A situation in which the variance of the error terms is not constant across observations (e.g. errors differ across farms or across years).
Serial correlation (autocorrelation): When the errors for the same farm are correlated over time (e.g. the error this year is related to the error last year)
Clustered standard errors: Standard errors adjusted to account for the correlation of observations within the same cluster – typically within farms (or regions) over time. This correction prevents underestimating uncertainty when residuals are correlated within clusters
Lagged outcome: A past value of the outcome variable (e.g. last year’s income) included as an explanatory variable to capture dynamic effects.

Step 5 – Interpret results carefully

Interpret FE estimates as within‑farm associations over time, net of all stable farm characteristics. Discuss any remaining risks of bias due to unobserved time‑varying factors. Where possible, benchmark FE estimates against simpler OLS models and more demanding causal approaches (e.g. DiD, GMM) to assess robustness.

Main takeaway points

FE models compare each farm to itself over time, removing bias from all characteristics that remain constant across farms.
They are especially suitable in CAP contexts with universal or widely applied measures and reliable panel data (e.g. FADN/FSDN).
FE improves on cross‑section OLS, but it does not fully resolve causal inference challenges, particularly when unobserved, time‑varying factors play a role.
Credible FE analysis requires a solid understanding of policy timing, data structure, and the remaining potential sources of bias.
FE is often one component of a broader mixed‑methods strategy, complemented where feasible by DiD, GMM, RDD or SCM.

Learning from practice

CAP direct payments and economic resilience of agriculture: impact assessment, Sustainability, 14(17), 10546.
His paper studies how CAP direct payments influence the economic resilience of agriculture in 27 EU countries (2005-2019). Resilience is measured through key industry functions, such as farm profitability, affordable food production, and jobs. A central empirical tool in the paper is the fixed effects (FE) estimator applied to panel data. FE models are used to estimate the impact of direct payments on different outcomes (e.g. agricultural production, food price ratio, agricultural profitability, wage employment, wages) while controlling for all unobserved and time-invariant national characteristics (such as institutions, altitude or location). Using FE, the authors focus on within-country changes over time, making the estimated effect of direct payments more reliable and less influenced by constant country-specific factors.
Petrick, M., & Zier, P., (2012), Common Agricultural Policy effects on dynamic labour use in agriculture, Food policy, 37(6), 671-678.
This paper analyses how different CAP measures influence agricultural employment in 69 East German regions using panel data. A key feature is the use of FE estimators to control for time-invariant and unobserved regional features (e.g. long-standing structural, institutional, or environmental differences between regions) that could influence policy impact estimates. Although several estimators are used (LSDV fixed effects, Blundell-Bond GMM, and bias-adjusted LSDV), the FE estimator is essential to address unobserved heterogeneity and obtain more credible estimates of how CAP measures influence labour use dynamics in agriculture.