Fixed effects model

Fixed effects model is a statistical technique used in the analysis of panel data, where multiple data observations are collected from the same subjects over a period of time. This model is designed to study the impact of variables that vary over time, controlling for all time-invariant characteristics of the individuals, whether observable or not. The key feature of the fixed effects model is its ability to control for unobserved heterogeneity when this heterogeneity is constant over time. This makes it particularly useful in econometrics, sociology, political science, and certain areas of medical research where longitudinal data is common.

Overview

In a fixed effects model, the assumption is that individual-specific effects, or intercepts, may not be correlated with the independent variables. This contrasts with random effects models, where such correlation is permitted. The choice between a fixed effects model and a random effects model often depends on the specific research question and the nature of the data. The Hausman test is frequently used to decide between these two models by testing the null hypothesis that the preferred model is random effects against the alternative fixed effects model.

Mathematical Formulation

The general form of a fixed effects model can be expressed as:

\[ y_{it} = \alpha + \beta X_{it} + \mu_i + \epsilon_{it} \]

where \(y_{it}\) is the dependent variable observed for individual \(i\) at time \(t\), \(X_{it}\) is a vector of independent variables, \(\alpha\) is the constant term, \(\beta\) represents the coefficients of the independent variables, \(\mu_i\) is the unobserved individual-specific effect, and \(\epsilon_{it}\) is the error term.

Application

Fixed effects models are widely used in fields that analyze panel data. In economics, they are used to study the effects of policy changes, economic conditions, or treatments over time at the individual or firm level. In sociology and political science, fixed effects models help in understanding the impact of social policies or political systems on individual behavior or outcomes over time. In medical research, these models can control for patient-specific characteristics when assessing the effectiveness of treatments or interventions over time.

Advantages and Disadvantages

The main advantage of the fixed effects model is its ability to control for all time-invariant characteristics, eliminating omitted variable bias due to those characteristics. However, this model cannot estimate the effects of time-invariant variables due to the removal of these effects in the transformation process. Additionally, fixed effects models require a large number of observations over time to provide reliable estimates, which can be a limitation in some research contexts.

See Also

• Panel data
• Random effects model
• Hausman test
• Longitudinal study
• Econometrics
• Sociology
• Political science
• Medical research

References

Fixed effects model Resources
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Fixed effects model Resources
Latest articles Most recent articles Ongoing trials	Wikipedia