quality:correction, information:filtering
Fixed effects estimator

Since α i {\displaystyle \alpha _{i}} is constant, α i ¯ = α i {\displaystyle {\overline {\alpha _{i}}}=\alpha _{i}} and hence the effect is eliminated. The FE estimator β ^ F E {\displaystyle {\hat {\beta }}_{FE}} is then obtained by an OLS regression of y ¨ {\displaystyle {\ddot {y}}} on X ¨ {\displaystyle {\ddot {X}}}.