In statistics and econometrics, panel data and longitudinal data are both multi-dimensional data involving measurements over time. Panel data is a subset of longitudinal data where observations are for the same subjects each time. Time series and cross-sectional data can be thought of as special cases of panel data that are in one dimension only. A study that uses panel data is called a longitudinal study or panel study.
Example
person
year
income
age
sex
1
2016
1600
23
1
1
2017
1500
24
1
2
2016
1900
41
2
2
2017
2000
42
2
2
2018
2100
43
2
3
2017
3300
34
1
In the example above, two datasets with a panel structure are shown. Individual characteristics are collected for different persons and different years. In the first dataset, two persons are observed every year for three years. In the second dataset, three persons are observed two times, three times, and one time, respectively, over three years ; in particular, person 1 is not observed in year 2018 and person 3 is not observed in 2016 or 2018. A balanced panel is a dataset in which each panel member is observed every year. Consequently, if a balanced panel contains N panel members and T periods, the number of observations in the dataset is necessarily. An unbalanced panel is a dataset in which at least one panel member is not observed every period. Therefore, if an unbalanced panel contains N panel members and T periods, then the following strict inequality holds for the number of observations in the dataset:. Both datasets above are structured in the long format, which is where one row holds one observation per time. Another way to structure panel data would be the wide format where one row represents one observational unit for all points in time or three rows of data with additional columns for each time-varying variable.
Analysis
A panel has the form where is the individual dimension and is the time dimension. A general panel data regression model is written as Different assumptions can be made on the precise structure of this general model. Two important models are the fixed effects model and the random effects model. Consider a generic panel data model: are individual-specific, time-invariant effects which are fixed over time., whereas is a time-varying random component. If is unobserved, and correlated with at least one of the independent variables, then it will cause omitted variable bias in a standard OLS regression. However, panel data methods, such as the fixed effects estimator or alternatively, the first-difference estimator can be used to control for it. If is not correlated with any of the independent variables, ordinary least squareslinear regression methods can be used to yield unbiased and consistent estimates of the regression parameters. However, because is fixed over time, it will induce serial correlation in the error term of the regression. This means that more efficient estimation techniques are available. Random effects is one such method: it is a special case of feasible generalized least squares which controls for the structure of the serial correlation induced by.
Dynamic panel data
Dynamic panel data describes the case where a lag of the dependent variable is used as regressor: The presence of the lagged dependent variable violates strict exogeneity, that is, endogeneity may occur. The fixed effect estimator and the first differences estimator both rely on the assumption of strict exogeneity. Hence, if is believed to be correlated with one of the independent variables, an alternative estimation technique must be used. Instrumental variables or GMM techniques are commonly used in this situation, such as the Arellano–Bond estimator.
