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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?

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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).

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