Random Effects Model

A random effects model utilizes repeated observations (i.e., panel data) to decompose and correct for within-group and between-group heterogeneity.

Description

This model is used for panel analysis.

A good starting point for modeling with panel data is the pooled OLS model. This model builds upon weaknesses of that methodology.

It is helpful to establish a decomposition for the unit error term ε_it into time-variant and time-invariant components: u_it and α_i. Strong assumptions about these variances are made. Importantly, there must be zero covariance between predictors and the error. With this, the covariance matrix of errors for the measurements all individuals i over time can be fully expressed in a T by T covariance matrix like:

Note that all off-diagonal coveriances are simply the within-group heterogeneity, the time-variant error. Furthermore, the covariance matrix for all individuals and all measurements can be fully expressed in a NT by NT covariance matrix like:

Note that all off-diagonal covariances are zero unless indiviuals i and j are the same.

The consequence of this specification is that errors can be estimated using a pooled OLS model.

CategoryRicottone