In time series data, one or several variables will be observed only in one unit of observation within a certain period of time. Meanwhile, cross-sectional data are observations from several units of observation at a certain point in time. Panel data is a combination of time series data and cross section data. In other words, panel data is data from several individuals who are observed over a certain period of time. If we have T time periods (t = 1,2,…,T) and N number of individuals (i = 1,2,…,N), then with panel data we will have a total of NT units of observation. If the number of time units is the same for each individual, then the data is called a balanced panel. However, if the number of time units is different for each individual, it is called an unbalanced panel. Regression that uses panel data is called Panel Data Regression.

There are 2 kinds of panel data regression equations, namely the One Way Model and the Two Way Model. One Way Model is a one-way model, because it only considers individual effects (αi) in the model. Two Way Model is a model that considers the effect of time or includes a time variable.

The Panel Data Regression method will provide estimation results that are Best Linear Unbiased Estimation (BLUE) if all Gauss Markov assumptions are met including non-autocorrelation. This non-autocorrelation is difficult to fulfill when we analyze panel data. So the parameter estimation is no longer BLUE. If the panel data is analyzed using time series models such as the transfer function, then there is information on the diversity of the cross-sectional units that is ignored in the modeling. One of the advantages of panel data regression analysis is considering the diversity that occurs in the cross section unit.

The advantages of performing panel data regression include:

Giving the researcher a large number of observations, increasing the degree of freedom, the data has a large variability and reducing the collinearity between the explanatory variables, which can produce efficient econometric estimates.
Panel data can provide more information that cannot be provided by only cross section or time series data.
Panel data can provide a better solution in dynamic change inference than cross section data.
The estimation method using panel data can be done through three approaches, including:

1. Common Effect Model or Pooled Least Square (PLS)
This is the simplest panel data model approach because it only combines time series and cross section data. This model does not pay attention to the dimensions of time or individuals, so it is assumed that the behavior of the observation data is the same in various time periods. This method can use the Ordinary Least Square (OLS) approach or the least squares technique to estimate the panel data model.

2. Fixed Effect Model (FE)
This model assumes that differences between individuals can be accommodated from differences in intercepts. To estimate panel data, the Fixed Effects model uses a dummy variable technique to capture the difference in intercepts between observations. However, the slope is the same between observations. This estimation model is often also called the Least Squares Dummy Variable (LSDV) technique.

3. Random Effect Model (RE)
This model will estimate panel data where disturbance variables may be interrelated over time and between individuals. In the Random Effect model, the difference in intercepts is accommodated by the error terms of each observation. The advantage of using the Random Effect model is that it eliminates heteroscedasticity. This model is also called the Error Component Model (ECM) or the Generalized Least Square (GLS) technique.

To choose the most appropriate model, there are several tests that can be done, including:

1. Chow test. Chow test is a test to determine whether the Common Effect (CE) or Fixed Effect (FE) model is the most appropriate for estimating panel data.

2. Hausman test. Hausman test is a statistical test to choose whether the Fixed Effect or Random Effect model is the most appropriate to use.

3. The Lagrange Multiplier (LM) test is a test to determine whether the Random Effect model is better than the Common Effect (PLS) method used.