There are many objects (i=1,…,n), which are observed at t=1,…,T time moments. Each object has k variables (attributes):
Most of panel data bases contain observations of a large number of objects for a relatively short period.
Suppose that:
- the dependent variable for i economical value at t time moment.
- the corresponding error.
In addition, there are "general" observations and errors:
This is a regular linear regression model:
in matrix form:
where β is the unknown vector of k×1 size.
Dependent variable is considered to be linearly dependent on all variables at the same time moment.
One can use the least-squares method to set up parameters:
The model is based on panel data structure, which enables the user to take into account immeasurable individual object differences. These differences are called effects.
This model regards effects as nuisance parameter and tries to exclude them.
The model is described with the following equation:
The 
value shows individual effect of the "i" object, independent of the "t" time, and the 
regressors do not contain any constant.
This model supposes that individual differences are random.
The model is described with the following equation:
See also:
Modeling Container: Panel Data Model | ISmPooledModel