# Is subtracting individual means in pre-processing an appropriate alternative to dummy variables for fixed effects panel data estimation?

Is subtracting individuals means during pre-processing of panel data exactly equivalent to including dummy variables for fixed effects estimation? If not, what are the differences, and is there some literature dealing with this?

When you subtract the individual means $$y_{it} - \overline{y}_{i} = (X_{it} - \overline{X}_i)\beta + \epsilon_{it} - \overline{\epsilon}_i$$ where $\overline{y}_{i} = \frac{1}{T}\sum^{T}_{t=1}y_{it}$, $\overline{x}_{i} = \frac{1}{T}\sum^{T}_{t=1}x_{it}$, and $\overline{\epsilon}_{i} = \frac{1}{T}\sum^{T}_{t=1}\epsilon_{it}$, and then run an OLS regression with the de-meaned variables then this is the fixed effects estimator. This is equivalent to including individual dummies in the regression which was shown by Mundlak (1978).