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| In [[statistics]] and [[econometrics]], the term '''panel data''' refers to multi-dimensional [[data set|data]] frequently involving measurements over time. Panel data contain observations of multiple phenomena obtained over multiple time periods for the same firms or individuals. In [[biostatistics]], the term '''longitudinal data''' is often used instead,<ref>{{cite book |first=Peter J. |last=Diggle |first2=Patrick |last2=Heagerty |first3=Kung-Yee |last3=Liang |first4=Scott L. |last4=Zeger |year=2002 |title=Analysis of Longitudinal Data |edition=2nd |location= |publisher=Oxford University Press |page=2 |isbn=0-19-852484-6 }}</ref><ref>{{cite book |first=Garrett M. |last=Fitzmaurice |first2=Nan M. |last2=Laird |first3=James H. |last3=Ware |year=2004 |title=Applied Longitudinal Analysis |location=Hoboken |publisher=John Wiley & Sons |page=2 |isbn=0-471-21487-6 }}</ref> wherein a subject or cluster constitutes a panel member or individual in a [[longitudinal study]].
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| [[Time series]] and [[cross-sectional data|cross-sectional]] data are special cases of panel data that are in one dimension only (one panel member or individual for the former, one time point for the latter).
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| ==Example==
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| {|
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| ! balanced panel: !! !! unbalanced panel:
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| |-
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| | <math>\begin{matrix}
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| \mathrm{person} & \mathrm{year} & \mathrm{income} & \mathrm{age} & \mathrm{sex}\\
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| 1 & 2001 & 1300 & 27 & 1 \\
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| 1 & 2002 & 1600 & 28 & 1 \\
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| 1 & 2003 & 2000 & 29 & 1 \\
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| 2 & 2001 & 2000 & 38 & 2 \\
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| 2 & 2002 & 2300 & 39 & 2 \\
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| 2 & 2003 & 2400 & 40 & 2
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| \end{matrix}</math>
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| |width=75px|
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| |<math>\begin{matrix}
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| \mathrm{person} & \mathrm{year} & \mathrm{income} & \mathrm{age} & \mathrm{sex}\\
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| 1 & 2001 & 1600 & 23 & 1 \\
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| 1 & 2002 & 1500 & 24 & 1 \\
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| 2 & 2001 & 1900 & 41 & 2 \\
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| 2 & 2002 & 2000 & 42 & 2 \\
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| 2 & 2003 & 2100 & 43 & 2 \\
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| 3 & 2002 & 3300 & 34 & 1
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| \end{matrix}</math>
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| |}
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| In the example above, two data sets with a two-dimensional panel structure are shown, although the second data set might be a three-dimensional structure since it has three people. Individual characteristics (income, age, sex. educ) 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.
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| ==Analysis of panel data==
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| A panel has the form
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| <math>X_{it}, \; i = 1, \dots, N \; t = 1, \dots, T, </math>
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| <br />
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| where <math>i</math> is the individual dimension and <math>t</math> is the time dimension. A general panel data regression model is written as <math>y_{it} = \alpha + \beta' X_{it} + u_{it}.</math>
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| 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]]. The fixed effects model is denoted as
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| : <math>y_{it} = \alpha + \beta' X_{it} + u_{it}, </math>
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| : <math>u_{it} = \mu_i + \nu_{it}.</math>
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| <math>\mu_i</math> are individual-specific, time-invariant effects (for example in a panel of countries this could include geography, climate etc.) and because we assume they are fixed over time, this is called the fixed-effects model. The random effects model assumes in addition that
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| : <math>\mu_i \sim \text{i.i.d.} N(0, \sigma^2_{\mu})</math>
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| and
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| : <math>\nu_{it} \sim \text{i.i.d.} N(0, \sigma^2_{\nu}),</math>
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| that is, the two error components are independent from each other.
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| ==Data sets which have a panel design==
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| * ''German'' [[Socio-Economic Panel]] (SOEP)
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| *[[Household, Income and Labour Dynamics in Australia Survey]] (HILDA)
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| *[[British Household Panel Survey]] (BHPS)
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| *[[Survey of Family Income and Employment]] (SoFIE)
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| *[[Survey of Income and Program Participation]] (SIPP)
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| *[[LLMDB|Lifelong Labour Market Database]] (LLMDB)
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| *[[Panel Study of Income Dynamics]] (PSID)
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| *[[Korean Labor and Income Panel Study]] (KLIPS)
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| *[[Chinese Family Panel Studies]] (CFPS)
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| *[[German Family Panel]] (pairfam)
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| *[[National Longitudinal Surveys]] (NLSY)
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| *[[National Longitudinal Surveys]] (NLSY)
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| *[[Labour Force Survey]] (LFS)
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| ==Data sets which have a multi-dimensional panel design==
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| {{Main|Multidimensional panel data}}
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| ==See also==
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| *[[Panel analysis]]
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| ==Notes==
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| {{reflist}}
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| ==References==
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| *{{cite book |last=Baltagi |first=Badi H. |year=2008 |title=Econometric Analysis of Panel Data |location=Chichester |publisher=John Wiley & Sons |edition=Fourth |isbn=978-0-470-51886-1 }}
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| *{{cite journal |last=Davies |first=A. |last2=Lahiri |first2=K. |year=1995 |title=A New Framework for Testing Rationality and Measuring Aggregate Shocks Using Panel Data |journal=[[Journal of Econometrics]] |volume=68 |issue=1 |pages=205–227 |doi=10.1016/0304-4076(94)01649-K }}
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| *{{cite book |last=Davies |first=A. |last2=Lahiri |first2=K. |year=2000 |chapter=Re-examining the Rational Expectations Hypothesis Using Panel Data on Multi-Period Forecasts |title=Analysis of Panels and Limited Dependent Variable Models |location=Cambridge |publisher=Cambridge University Press |isbn=0-521-63169-6 |pages=226–254 }}
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| *{{cite book |last=Frees |first=E. |year=2004 |title=Longitudinal and Panel Data: Analysis and Applications in the Social Sciences |location=New York |publisher=Cambridge University Press |isbn=0-521-82828-7 }}
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| *{{cite book |last=Hsiao |first=Cheng |year=2003 |title=Analysis of Panel Data |location=New York |publisher=Cambridge University Press |edition=Second |isbn=0-521-52271-4 }}
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| ==External links==
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| *[http://psidonline.isr.umich.edu/ PSID]
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| *[http://www.kli.re.kr/klips KLIPS]
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| *[http://www.pairfam.uni-bremen.de/en/study.html pairfam]
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| [[Category:Econometrics|P]]
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| [[Category:Multivariate statistics]]
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| [[Category:Statistical data types]]
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| [[Category:Panel data| ]]
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