Panel data analysis is a statistical method that allows researchers to study the effects of variables that vary over time and across individuals or groups. Panel data analysis can help answer questions such as how does income affect health outcomes, how do policies affect economic growth, or how do individual preferences change over time.

In this article, we will explain what panel data is, how to declare panel data in Stata, and how to choose between different estimators for panel data models. We will also provide some examples of panel data analysis using Stata.

Panel data, also known as longitudinal data or cross-sectional time-series data, is a type of data that consists of repeated observations of the same units over time. For example, panel data can be collected from a sample of individuals who are surveyed every year, a sample of countries that report their economic indicators every quarter, or a sample of firms that disclose their financial statements every month.

Panel data has two dimensions: the cross-sectional dimension (N) and the time dimension (T). The cross-sectional dimension refers to the number of units (individuals, countries, firms, etc.) in the sample, while the time dimension refers to the number of periods (years, quarters, months, etc.) for which each unit is observed. The total number of observations in a panel dataset is N*T.

Panel data can be balanced or unbalanced. Balanced panel data means that each unit is observed for the same number of periods, while unbalanced panel data means that some units are observed for more or fewer periods than others. For example, if we have a panel dataset of 100 individuals who are surveyed every year from 2010 to 2020, then we have a balanced panel with N=100 and T=11. However, if some individuals drop out of the survey or join later, then we have an unbalanced panel with N<100 and T<11 for some units.

When we work with panel data in Stata, we need to declare that we have a panel dataset. This tells Stata how to identify the units and the periods in the data and how to handle missing values and gaps in the data. To declare panel data in Stata, we use the xtset command. The syntax of the xtset command is:

xtset idvar [timevar] [ , options ]

The idvar is the variable that identifies the cross-sectional units in the data. The timevar is the variable that identifies the time periods in the data. The options are optional arguments that specify how to treat missing values and gaps in the data.

For example, suppose we have a panel dataset of 50 countries that report their GDP per capita and life expectancy every year from 2000 to 2019. The dataset has three variables: country, year, and gdp_pc. To declare this dataset as panel data in Stata, we type:

xtset country year

This tells Stata that country is the variable that identifies the cross-sectional units and year is the variable that identifies the time periods. Stata will then display some information about the panel structure of the data, such as:

Panel variable: country (strongly balanced)
 Time variable: year, 2000 to 2019
         Delta: 1 unit

This indicates that we have a strongly balanced panel with N=50 and T=20 and no missing values or gaps in the data.

Once we have declared our panel data in Stata, we can estimate various models using panel data methods. The most common model for panel data analysis is the linear regression model with one or more explanatory variables. The general form of this model is:

y_it = alpha + beta*x_it + u_it