In
statistics and
econometrics
Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8 ...
, panel data and longitudinal data
are both multi-dimensional
data
In the pursuit of knowledge, data (; ) is a collection of discrete Value_(semiotics), values that convey information, describing quantity, qualitative property, quality, fact, statistics, other basic units of meaning, or simply sequences of sy ...
involving measurements over time. Panel data is a subset of longitudinal data where observations are for the same subjects each time.
Time series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Ex ...
and
cross-sectional data
Cross-sectional data, or a cross section of a study population, in statistics and econometrics, is a type of data collected by observing many subjects (such as individuals, firms, countries, or regions) at the one point or period of time. The anal ...
can be thought of as 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).
A study that uses panel data is called a
longitudinal study
A longitudinal study (or longitudinal survey, or panel study) is a research design that involves repeated observations of the same variables (e.g., people) over short or long periods of time (i.e., uses longitudinal data). It is often a type of ob ...
or panel study.
Example
In the multiple response permutation procedure (MRPP) example above, two datasets with a panel structure are shown and the objective is to test whether there's a significant difference between people in the sample data. Individual characteristics (income, age, sex) are collected for different persons and different years. In the first dataset, two persons (1, 2) are observed every year for three years (2016, 2017, 2018). In the second dataset, three persons (1, 2, 3) are observed two times (person 1), three times (person 2), and one time (person 3), respectively, over three years (2016, 2017, 2018); in particular, person 1 is not observed in year 2018 and person 3 is not observed in 2016 or 2018.
A balanced panel (e.g., the first dataset above) is a dataset in which ''each'' panel member (i.e., person) is observed ''every'' year. Consequently, if a balanced panel contains ''N'' panel members and ''T'' periods, the number of observations (''n'') in the dataset is necessarily .
An unbalanced panel (e.g., the second dataset above) 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 (''n'') 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 (for the example, the wide format would have only two (first example) or three (second example) rows of data with additional columns for each time-varying variable (income, age).
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
In statistics, a fixed effects model is a statistical model in which the model parameters are fixed or non-random quantities. This is in contrast to random effects models and mixed models in which all or some of the model parameters are random ...
and the
random effects model
In statistics, a random effects model, also called a variance components model, is a statistical model where the model parameters are random variables. It is a kind of hierarchical linear model, which assumes that the data being analysed are dra ...
.
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
In statistics, generalized least squares (GLS) is a technique for estimating the unknown parameters in a linear regression model when there is a certain degree of correlation between the residuals in a regression model. In these cases, ordinar ...
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.
Data sets which have a panel design
*
Russia Longitudinal Monitoring Survey (RLMS)
* ''German''
Socio-Economic Panel
The ''German'' Socio-Economic Panel (SOEP [], for ''Sozio-oekonomisches Panel'') is a Longitudinal study, longitudinal panel dataset of the population in Germany. It is a household based study which started in 1984 and which reinterviews adul ...
(SOEP)
*
Household, Income and Labour Dynamics in Australia Survey
The Household, Income and Labour Dynamics in Australia (HILDA) survey is an Australian household-based panel study which began in 2001. It has been used for examining issues such as the incidence of persistent poverty; assets and income in the t ...
(HILDA)
*
British Household Panel Survey
The British Household Panel Survey (BHPS), carried out at the Institute for Social and Economic Research of the University of Essex, is a survey for social and economic research. A sample of British households was drawn and first interviewed in ...
(BHPS)
*
Survey of Family Income and Employment (SoFIE)
*
Survey of Income and Program Participation (SIPP)
*
Lifelong Labour Market Database (LLMDB)
Longitudinal Internet Studies for the Social sciences (LISS
*
Panel Study of Income Dynamics The Panel Study of Income Dynamics (PSID) is a longitudinal panel survey of American families, conducted by the Survey Research Center at the University of Michigan.
The PSID measures economic, social, and health factors over the life course of f ...
(PSID)
*
Korean Labor and Income Panel Study
Korean may refer to:
People and culture
* Koreans, ethnic group originating in the Korean Peninsula
* Korean cuisine
* Korean culture
* Korean language
**Korean alphabet, known as Hangul or Chosŏn'gŭl
**Korean dialects and the Jeju language
** ...
(KLIPS)
*
China Family Panel Studies
China Family Panel Studies (CFPS, zh, 中国家庭追踪调查) is a nationally representative, biennial longitudinal general social survey project designed to document changes in Chinese society, economy, population, education, and health. The ...
(CFPS)
*
German Family Panel
German(s) may refer to:
* Germany (of or related to)
**Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizens of Germany, see also German nationality law
**Ger ...
(pairfam)
*
National Longitudinal Surveys
The National Longitudinal Surveys (NLS) are a set of surveys sponsored by the Bureau of Labor Statistics (BLS) of the U.S. Department of Labor. These surveys have gathered information at multiple points in time on the labor market experiences an ...
(NLSY)
*
Labour Force Survey
Labour Force Surveys are statistical surveys conducted in a number of countries designed to capture data about the labour market. All European Union member states are required to conduct a Labour Force Survey annually. Labour Force Surveys are als ...
(LFS)
*
Korean Youth Panel
Korean may refer to:
People and culture
* Koreans, ethnic group originating in the Korean Peninsula
* Korean cuisine
* Korean culture
* Korean language
**Korean alphabet, known as Hangul or Chosŏn'gŭl
**Korean dialects and the Jeju language
** ...
(YP)
*
Korean Longitudinal Study of Aging
Korean may refer to:
People and culture
* Koreans, ethnic group originating in the Korean Peninsula
* Korean cuisine
* Korean culture
* Korean language
**Korean alphabet, known as Hangul or Chosŏn'gŭl
**Korean dialects and the Jeju language
** ...
(KLoSA)
Data sets which have a multi-dimensional panel design
Notes
References
*
*
*
*
*{{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
External links
PSIDKLIPSKorea Employment Survey
P
Statistical data types
Mathematical and quantitative methods (economics)