Panel analysis

Panel (data) analysis is a statistical method, widely used in <a href="/facts/Social_science/hAbm1xtD">social science</a>, <a href="/facts/Epidemiology/wgTmxoMA">epidemiology</a>, and <a href="/facts/Econometrics/7U52gzHt">econometrics</a> to analyze two-dimensional (typically cross sectional and longitudinal) <a href="/facts/Panel_data/5cHTwLe9">panel data</a>. The data are usually collected over time and over the same individuals and then a <a href="/facts/Linear_regression/5n998IhK">regression</a> is run over these two dimensions. <a href="/facts/Multidimensional_analysis/1epd7zfc">Multidimensional analysis</a> is an <a href="/facts/Econometrics/7U52gzHt">econometric</a> method in which data are collected over more than two dimensions (typically, time, individuals, and some third dimension).
A common <a href="/facts/Panel_data/5cHTwLe9">panel data</a> regression model looks like 
 
 
 
 
 y
 
 i
 t
 
 
 =
 a
 +
 b
 
 x
 
 i
 t
 
 
 +
 
 ε
 
 i
 t
 
 
 
 
 {\displaystyle y_{it}=a+bx_{it}+\varepsilon _{it}}
 
, where 
 
 
 
 y
 
 
 {\displaystyle y}
 
 is the <a href="/facts/Dependent_variable/dINfzIF2">dependent variable</a>, 
 
 
 
 x
 
 
 {\displaystyle x}
 
 is the <a href="/facts/Independent_variable/dINfzIF2">independent variable</a>, 
 
 
 
 a
 
 
 {\displaystyle a}
 
 and 
 
 
 
 b
 
 
 {\displaystyle b}
 
 are coefficients, 
 
 
 
 i
 
 
 {\displaystyle i}
 
 and 
 
 
 
 t
 
 
 {\displaystyle t}
 
 are <a href="/facts/Indexed_family/aFqfzJN0">indices</a> for individuals and time. The error 
 
 
 
 
 ε
 
 i
 t
 
 
 
 
 {\displaystyle \varepsilon _{it}}
 
 is very important in this analysis. Assumptions about the error term determine whether we speak of fixed effects or random effects. In a fixed effects model, 
 
 
 
 
 ε
 
 i
 t
 
 
 
 
 {\displaystyle \varepsilon _{it}}
 
 is assumed to vary non-stochastically over 
 
 
 
 i
 
 
 {\displaystyle i}
 
 or 
 
 
 
 t
 
 
 {\displaystyle t}
 
 making the fixed effects model analogous to a dummy variable model in one dimension. In a random effects model, 
 
 
 
 
 ε
 
 i
 t
 
 
 
 
 {\displaystyle \varepsilon _{it}}
 
 is assumed to vary stochastically over 
 
 
 
 i
 
 
 {\displaystyle i}
 
 or 
 
 
 
 t
 
 
 {\displaystyle t}
 
 requiring special treatment of the error variance matrix.
Panel data analysis has three more-or-less independent approaches:

<ul><li>independently pooled panels;</li>
<li><a href="/facts/Random_effects_model/FnWmvRsc">random effects models</a>;</li>
<li><a href="/facts/Fixed_effects_estimator/L5JPDQnB">fixed effects models</a> or first differenced models.</li></ul>
The selection between these methods depends upon the objective of the analysis, and the problems concerning the exogeneity of the explanatory variables.

Panel analysis open-in-new

Panel analysis