Fixed effects model

In statistics the Fixed effects estimator is an estimator for the coefficients in panel data analysis. If we assume fixed effects, we impose time independent effects for each individual.

Formally the model is

$y_{it}=X_{it}\beta +\alpha _{i}+u_{it}$,

where $y_{it}$ is the dependent variable observed for individual i at time t, $\beta$ is the vector of coefficients, $\alpha _{i}$ is the individual effect and $u_{it}$ is the error term.

and the estimator is

Failed to parse (syntax error): {\displaystyle \beta=\left(x_{i}'{x_{i} \right)^{-1}\left(x_{i}'y_{i} \right)} ,

where $x_{i}$ is the demeaned regressor ($x_{i}=x_{it}-{\hat {x_{it}}}$) and $y_{it}$ is the demeaned dependent variable ($y_{i}=y_{it}-{\hat {y_{it}}}$).

See also

Random effects estimator

Literature

Source