In statistics and econometrics, panel data or longitudinal data are multi-dimensional data involving measurements over time. Panel data contain observations of multiple phenomena obtained over multiple time periods for the same firms or individuals
|balanced panel:||unbalanced panel:|
In the example above, two data sets with a panel structure are shown. Individual characteristics (income, age, sex) are collected for different persons and different years. In the left data set two persons (1, 2) are observed over three years (2001, 2002, 2003). Because each person is observed every year, the left-hand data set is called a balanced panel, whereas the data set on the right hand is called an unbalanced panel, since person 1 is not observed in year 2003 and person 3 is not observed in 2003 or 2001. This specific structure these data sets are in is called long format 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 (for the example, the wide format would have only two (left example) or three (right example) rows of data with additional columns for each time-varying variable (income, age). Representing panel data in long format is much more common than using the wide format because it saves storage space. This is due to the fact that wide format will have lots of sparse cells wasting storage space.
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 (for example in a panel of countries this could include geography, climate etc.) 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 squares linear 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 describe 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 dependent 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.
Data sets which have a panel design
- Russia Longitudinal Monitoring Survey (RLMS)
- German Socio-Economic Panel (SOEP)
- Household, Income and Labour Dynamics in Australia Survey (HILDA)
- British Household Panel Survey (BHPS)
- Survey of Family Income and Employment (SoFIE)
- Survey of Income and Program Participation (SIPP)
- Lifelong Labour Market Database (LLMDB)
- Panel Study of Income Dynamics (PSID)
- Korean Labor and Income Panel Study (KLIPS)
- Chinese Family Panel Studies (CFPS)
- German Family Panel (pairfam)
- National Longitudinal Surveys (NLSY)
- Labour Force Survey (LFS)
- Korean Youth Panel (YP)
- Korean Longitudinal Study of Aging (KLoSA)
Data sets which have a multi-dimensional panel design
- Diggle, Peter J.; Heagerty, Patrick; Liang, Kung-Yee; Zeger, Scott L. (2002). Analysis of Longitudinal Data (2nd ed.). Oxford University Press. p. 2. ISBN 0-19-852484-6.
- Fitzmaurice, Garrett M.; Laird, Nan M.; Ware, James H. (2004). Applied Longitudinal Analysis. Hoboken: John Wiley & Sons. p. 2. ISBN 0-471-21487-6.
- Baltagi, Badi H. (2008). Econometric Analysis of Panel Data (Fourth ed.). Chichester: John Wiley & Sons. ISBN 978-0-470-51886-1.
- Davies, A.; Lahiri, K. (1995). "A New Framework for Testing Rationality and Measuring Aggregate Shocks Using Panel Data". Journal of Econometrics. 68 (1): 205–227. doi:10.1016/0304-4076(94)01649-K.
- Davies, A.; Lahiri, K. (2000). "Re-examining the Rational Expectations Hypothesis Using Panel Data on Multi-Period Forecasts". Analysis of Panels and Limited Dependent Variable Models. Cambridge: Cambridge University Press. pp. 226–254. ISBN 0-521-63169-6.
- Frees, E. (2004). Longitudinal and Panel Data: Analysis and Applications in the Social Sciences. New York: Cambridge University Press. ISBN 0-521-82828-7.
- Hsiao, Cheng (2003). Analysis of Panel Data (Second ed.). New York: Cambridge University Press. ISBN 0-521-52271-4.